This is none of my business, but I am intrigued by this arrangement - it sounds totally fine for two people without a child, but with a baby?
Have you agreed how long you are planning to take off work initially, and thereafter (i.e once the baby is older than 9 months or so?)? And are you planning on returning to full time work and sending your DC to full time nursery, or working part time/flexi time or similar? How much are you/your DP expecting that he will help out with the baby when he is around?
Just that these decisons are huge! emotionally and financially. And they have a very big impact on a couple, so if you have a partner who doesn't live with you and is reluctant to talk about money issues... how do they think it is going to work, exactly?
I don't know that it is necessarily a problem that father and mother won't be living together full time (after all, mums have partners who work on oil rigs or abroad, it's not totally unheard of) - it's just that it doesn't sound, to me, forgive me, as if you are in a co-parent relationship with this man. And I may be confusing posters here - but early days with a newborn can be really stressful, feeling isolated makes it so much harder - and unless you have discussed things and know you can rely on your partner, then it's easy for things to end up on the rocks.
I don't like the sound of a partner who doesn't have savings or own property (nothing wrong with that in itself at all, but where the woman does and the man doesn't, I think 'hmmm') - or like discussing money or big issues.
Btw, I'm self employed too. We tend to be very self starting 'get up and do it' people - but if you have a more passive partner, who contributes a lot less to the family finances AND will not be very present - this may have been the template of your relationship so far, but I would be prepared to countenance some very big changes once a baby is in the mix.