My very best advice to you at this point, is to do NOTHING. Let your realizations really sink in. Give yourself some breathing room. The very worst thing you could do right now is make knee-jerk decisions, or run off in the opposite direction.
Doing NOTHING at this point allows the dust to settle. Stop thinking for awhile, stop assessing, and just live. Just observe. Perhaps keep a daily journal and just record thoughts. Your mind, at this point, is rewiring itself. Give it and yourself time. Be nice to yourself. It's OKAY.
You'll know when the dust settles. This doesn't mean you will kick H to the curb. It doesn't mean you won't. My advice to you is that whatever decisions and discussions you have with your H, it is best done with a clear head, and a clear understanding of this acceptance you are now going through. It puts you in an AMAZING position.