Oh, this is not right. I am in a relationship with my girlfriend and husband, so I understand the difficulties splitting up household chores in a triad.
Do you have a concrete list of chores, divided by person? This can really help, especially when one person is at home all the time, then they don't feel like they are expected to do everything just because they dont work outside the house.
I also favor the idea of individual accounts for spending money. It really prevents a lot of butt-hurt. If he spends out his weekly allotment, then he's done. We also have a policy where no one touches the main account without discussion first. Each pay cycle we transfer a certain amount into each of the three mini-checking accounts. Since she and I do the bulk of grocery shopping, we decide how much to use from the main account for that purpose, and all other bills are auto deductions.
As for the introductions, I'm surprised he's not more protective of his family! We are very protective of each other and try not to rock the boat in new situations. We realize what an anomaly we are and don't rub it in people's faces. If pressed we tell the truth, but to a stranger at a get together, we say 'this is our best friend, she's part of the family' and leave it at that. This is especially important as we have children to protect.
I think you need a family meeting, to re-prioritize things and get everyone on the same page.