Not really sure exactly how it works when one of you only is a student but I can explain how things work for DH and I (both full time students with dependents).
During term time we have an underlying entitlement to Housing Benefit but our loans are classed as too much money for this to be paid. We also get child benefit and child tax credit (which gives us free dental care, eye care and prescriptions(free in Scot anyway)) during term time. And as I am pregnant we now get healthy start vouchers too.
During the summer months we are classed as having no income so we actually receive housing benefit and my DH claims job seekers allowance for us both as we don't qualify for income support (youngest child is too old I believe).
Not sure if that will change this summer as we will have a newborn. Will have to wait and see.
We are exempt from council tax due to both being students but I do know that your partner would reduce you CT by 25% and it would still only be you liable for paying that.
Entitlement to your existing benefits would completely depend on his income and what they consider in their calculations. It is different in England and scotland too I believe as to what counts as a loan or a grant etc and as such what is included as qualifying amounts which could affect your benefits.
The most difficult thing we found was that many job centre/benefit office employees are not used to complex cases involving students so we found it hard to get the right advice. Do as much reading as you can though so you can be informed. We got fobbed off a lot at the beginning, especially when we tried to claim free school meals for our DD as we'd been working full time the year before so they said we weren't entitled. That was nonsense btw!
Also don't let anyone make you feel judged. The benefit system is there to help people. The media likes to give it, and those who use it, a bad name but unfortunately it's needed in order to survive or get ahead sometimes. I know that DH and I would not be pursuing our degrees of social work and medicine respectively without benefits! We are both the first in our families to go to university, albeit later in life, so there's no way we could survive without assistance.
Good luck and congrats :)