Yes. As far as I know you get a referral from your PCM for it, but his pedi might be able to do it for you. I would call Tricare and ask what they need for it to be covered.
If you are still in Michigan then call Tricare North - 1-877-874-2273 - or call the number for whatever region you are in. There is an option for mental health services. You don't need to get a referral from your PCM.
I had PPD this past year and called, set up an appointment and was able to see someone quickly. You automatically get 8 visits and then if you need more sessions your psychologist/psychiatrist can request additional sessions. I was even able to bring my baby with me when I didn't have someone to watch her! (My psychologist was awesome).
Good luck and I hope you are able to heal soon! You are not alone so if you have any questions, let me know!
I work in a psychologist's office and have Tricare, so here's a bunch of info-
Do you want medication for PPD or therapy? If medication, your MTF family doctor will probably be the best first stop, they can prescribe initial psychotropics and start you on the process. If you don't respond to the first med or two, they might send you off-base to a psychiatrist because that's their specialty. Not many psychiatrists (in my area at least) do therapy.
If you want therapy, I agree with PPs- call your local Tricare region and go to their Mental Health option. They farm out their mental health work, in the South region it goes to Value Options but I'm not sure about other regions. You will probably see an LCSW (licensed clinical social worker) or LMHC (licensed mental health counselor) rather than a psychologist, because psychologists charge more for therapy, but depending on who is available they will have a list of local providers who take Tricare and are accepting new patients.
(Really) long story short- it's covered. Good luck and I hope you find an option that works out for you ASAP!