basically, as Christians, we don't believe it's ok to live together without being married.
also, we don't think it's a good idea for Christians to marry those who are not Christians because of this whole thing u r experiencing, which is that it's really painful not to be able to share the most important thing in yr life (which is faith, for those who are Christian) with the most important person in yr life who is yr partner (in most cases).
so, the way i see it, is u have to assess whether u are both basically 'married' already, in which case legalise it (in a civil wedding, for example) or u have to decide that there are too many differences and move on (which feels like a divorce even if u are not technically married; only u can decide if this is an option for u).
the church (in my understanding) will not pressure anyone who is civilly married to get a divorce, as they recognise the union even if does not take place in church, and then they will approach u as a Christian already married to a non Christian and baptise u alone.
the downside of this approach is that yr fiance may decide to stay non Christian indefinitely and then u will have to accept this outcome.
but the church can't agree to a church member living with someone they are not married to. (i mean 'living with'
not just flat mates) also after u r baptised, if yr fiance decides not to follow u, u will not be 'allowed' to marry him after u r baptised. i say 'allow' coz of course anyone can get a civil wedding, but u will not be admitted into the full live of the church (eg. communion) if u marry a non Christian after being baptised.
these rules sound harsh, but they are there to protect people's hearts. it is truly difficult to have a partner who does not share yr faith, unless yr faith is not important to u. i am assuming yr faith is important to u, as u would not be making the effort to convert 'just for fun'! (well maybe some very very bored people do, but i think it is not yr case).
so i think u have to honest about the situation with yr fiance and see where that leads. maybe u will both be baptised, maybe u will run off and get married and risk the possible lifelong differences (and possibly upset the priest, thus delaying baptism), or maybe u will both slow down and arrange for u to be baptised a bit later when u have both had more time to think and consider yr options. i have several friends who have had interesting marital situations in the church, so if u need more advice from someone who has considered these things a lot, please send a personal message.
may God guide u.