I am not so sure “European” is the qualifying factor; I guess there will be many answers in the comments
I’m working for a European bank which will pretty much pay for 100% of my outpatient medical expenses, and those of my wife and children. It doesn’t matter whether I see a general practitioner or a specialist. I am also free to choose any clinic I like (in other words, I don’t have to go to a pre-approved list of panel doctors).
My employer will also cover the medical expenses of an employee’s partner, regardless of whether they are married or not. As a matter of fact, my employer will cover the medical expenses of the employee’s gay partner. Also, if I remember correctly, my employer will cover the medical expenses of your illegitimate children (but I think that there are some rules on the maximum number of illegitimate children permissible).