Marsha,
That is an interesting question and much will depend upon what your state requirements are for high school (and also what type of higher education plans you have for your child as to whether that child is college bound, etc).
For a distinguished track high school education, most states are moving toward a 4 x 4 requirement for serious college-bound students who wish to compete for scholarships. This includes requiring 4 years of science (with 3 of the years being a lab science and typically including Biology and Chemistry at a minimum), 4 years of literature study/grammar/composition combo. (with American lit. being a requirement for sure and some leeway in the other literature areas), 4 years of history (typically covering geography a year or at least a semester, world history a year, American history a year, and Economics or Finance/Government each for a semester - although you can do various combinations to reach these requirements), and 3-4 years of math (with a bare minimum of algebra and geometry). There are other additional areas that are typically required as well like speech, fine arts, physcical education, computer, 2 consecutive years of a foreign language, etc. however the 4 x 4 requirements will take the bulk of the time.
If your student is not college-bound or is headed toward community college, you would have more leeway in the requirements and would instead focus on the basic requirements of the state and on fine-tuning a course of study that will guide your child in training for his/her future goals.
As far as CTC goes, in order to count it for high school credit, you'd need to up the level of reading material for history by adding more high-school worthy reading. You could add something like
Unwrapping the Pharaohs for the first section of study for Egypt, and look for some upper level materials for Greece and Rome as well. This is a tough time period to find God-honoring content though, even in upper level material. We have some pretty major problems with much of the material out there for this time period.

Another thought would be to do a geography year or semester course (depending on whether your state requires a semester or a year of geography) using Ellen McHenry's
Mapping the World by Art for geography credit, and then not worrying about the history credit for this year. You could add this daily to CTC and get through the study in a year. Yesterday's Classics has a book by Synge that will pair well with the Mapping the World by Art to add more content reading for geography. We are looking at doing this with our own son in grade 9 and moving toward possibly writing a geography guide someday for grade 9 utilizing these resources among others.
If you went the history credit route instead (upping the history readings), the geography within CTC alone would likely be 1/4 credit of your total geography needed for high school, as you'd be doing some geography each year to add together for your geography credit by the time your child is a senior. In that respect, the geography would likely be fine from CTC. The geography portion in our upcoming RTR will be strong too, so you'd likely be alright if you kept on this same path of upping each level of HOD for your high school child.
You'd also want to make sure your child is reading higher level literature, doing this either through choosing higher level books that match the time period (or any books you choose) to add to DITHR or by utitlizing a different literature program instead. DITHR is worthy of high school credit in lit. for grade 9, depending on which books you select for use along with it. Since we've used DITHR for years for my oldest son, we're moving into something else in high school for lit. study. We have looked long and hard for one that we like for our own son next year and have been having a tough time finding one that meets all of our goals. We are leaning toward doing much of Smarr's Intro. to Lit. course at this point, however we prefer Write with the Best Vol. II to use with it for grade 9 comp., rather than Smarr's writing lessons (at the 9th grade level anyway).
If your oldest child has not done Write with the Best Vol. I, then you could begin by doing that for high school comp. for a semester first in grade 9 (or as its scheduled within CTC instead if you want a slower pace) and moving toward Write with the Best Vol. II the second semester of grade 9 or the next year. Write with the Best I is on the easy side for high school but is a good intro. for students who have had little writing practice. Write with the Best II is fine for grade 9 writing. Both could be 9th grade worthy composition programs when combined with literature study and grammar instruction. Or, you could just add your own program for comp. that fits your child best.
For grammar, we are leaning toward continuing with Rod and Staff for high school, doing English 7 during grades 9-10 (half each year) and doing English 8 in grade 11-12 (half each year). These two levels are definitely high school worthy in their Table of Contents and in their coverage. You could use any grammar option with which you feel comfortable, although I'd lean toward doing some grammar every year as many sections of the SAT/ACT are a reflection of what is covered under the "English" umbrella.
You would definitely need to add or use something else for science in looking for biology credit and lab credit. However, whatever you use for biology would dovetail nicely with the Life Science/ Biology focus in CTC.

If you were looking for a lighter science approach you could consider adding the Biology 101 DVD and its outlined requirements for biology credit. Otherwise, you could use any of the other standard biology offerings (i.e. Apologia, BJU, CLP, etc.). We are leaning toward PAC-works Biology and Anatomy and Physiology doing a lesson a day 4 days a week with a lab on Fridays. We're thinking of using some of Castle Heights Biology labs for our own son next year at this point.
For Bible credit, you could add something like
Balancing the Sword to the Bible Quiet Time readings within CTC. This would add time to that component to make it credit worthy and raise the level of the material, while giving some good thought-provoking questions to go with the Bible reading.

We are planning to use this with our own son for high school Bible study.
I have to run for now, but this will get the ball rolling on some thinking of what you could do for high school with CTC.
Blessings,
Carrie