Had a new baby recently and having lots of arguments with partner about responsibilities. I work and they don't but they think I should be taking more care of the baby. When I'm not at work I already do look after the baby and we take it in turns at night. It's really frustrating - they don't seem to like being a parent and want to ruin my work. Money isn't a problem and we have the option of a nanny but partner would rather argue and blame me for not helping. We have no relatives or good enough friends nearby that can help either.
Are they being unreasonable not wanting to take care of the baby and just go socialize/gym/etc? I'm trying to compromise but it's driving me mad with the constant demands 
Any suggestions?