SO and I are moving in together in the next couple of months. We agreed on splitting things proportionately to our income, which works out to me paying 60% of our shared expenses and she covering the other 40%. What this does is keep our savings rate roughly equal, although the dollar amounts are different. In this case, if we both started with $0 in our stash we'd reach FI around the same time.
To level set with that, if I go grocery shopping I'm never going to ask her for money. We take turns buying groceries. Gas, insurance, cell phones are all separate. Sometimes she covers the bill if we go out to eat, other times I do. I'm not even sure I'll ask her to help pay for the internet or utilities because doing so isn't a huge setback for me, assuming the utility bill doesn't double*. Plus, I'd have to pay them with or without her there. Plus plus, SO makes great food so I'm happy to pay for groceries. She does all the difficult kitchen stuff. :)
*She basically lives rent free with me now and her being there hasn't impacted my utility bill.