Hi, good to see your first post.
Before tackling your question, can I ask if you have or have applied for a Certificate of Approval to Register a Civil Partnership? If not you certainly need to get a CoA before you and your partner go along to the Register Office to give the Notice of Intention to Register a Civil Partnership. This is the case because you are a non-EEA citizen and here in the UK on an employment visa.
If the CoA has not yet been applied for, can I ask, when does your employment visa expire?
OK, your question. Your partner
is entitled to get a Residence Permit in his passport and based upon that fact you should be able to get one based upon the fact that you will be a "family member".
Firstly, your partner's ability to get a Residence Permit even though he is in the UK as a student. This is covered by Chapter 1 of the IND instructions given to its staff dealing with EEA matters. The IND website is horrendous slow at the moment (otherwise this answer would have been posted much earlier) but you can download Chapter 1 from elsewhere on the internet by
clicking here. In particular look at 6 in that chapter.
The Family Member issue is dealt with by Chapter 2 .....
click here.
As I read those instructions both Residence Permits will expire when your partner will cease to be a student in the UK. However if he then intends to work in the UK, as will be his right under EEA regulations, both of you will be able to get new Residence Permits at that time.
Hope this helps.