This is not easy and not standard but possible.
Your problem is, that you have in fact 2 websites with different session-ids/cookies.
I suppose you want to get authentication and you probably do not want to transfer any password in cleartext.
Thatwhy I would invent some token which might unlock your user on the non-https-website with help of some https-website.
What I would do:
I would invent some token that I generate on a hash over his session-id, some text and some construction containing the actual date or year. Or just some random number as Token.
You save this token to your database and the users non-https-session. Then send the user to the HTTPS-Site with your login-procedure. https://ssl.example.com/?token=234987239427839428347
If the user can verify his account with his password, you unlock the row with this token in your database. Then you send the user back to your non-https-site.
Whenever some user visits your non-https-site (with generated token and not logged in) you should look for an unlocked token which the session knows. In case that this token is unlocked and correct just log the user in.
This is a solution, it is sure possible but you might think about your initial intentions to do it.
Non-HTTPS is nothing that I would personally suggest. But as a webmaster I know the thing with ads and other things that would prevent me to force my users to surf on https. Thatwhy I just gave them a choice. And they dont really care for HTTPS. But some love it.