I agree with waht everyone else has said. I am almost finished with EHE - my two are 18 and almost 16 and have been EHE from birth.
Looking back, I wouldn't change the basic decision (although there are things I'd do differently now I know - waiting for grandchildren to do it properly, LOL).
Do you enjoy it?
Yes. Still.
Is it expensive?
Like others, I spent too much in the early years on stuff that I thought we needed and then didn't use. I'd go for Just-In-Time purchasing - if you want to use it NOW, buy it; otherwise, file the fact of its existence away in your head for future.
During primary years, we bought minimal clothes (still do! and none of them are "special" for weekdays). We paid for swimming, drama and kids' clubs - but we'd have done that, anyway, even if they'd been in school. We also bought craft materials. They started instrumental lessons at 11 and 10 (if I had my time over, I'd do more with music at younger ages) but, again, we'd have had to pay even if they were in school.
At secondary age, the big expense is getting qualifications. Some people use school at that point. Others do GCSEs at home, however, EHEers have the freedom to choose only to do the qualifications they need. For example, most colleges seem to accept people onto A-level courses with five good GCSEs, so people can choose only to do the five required. My DD has a conditional offer for university in October. We knew she was looking at uni, so we decided to bypass GCSEs/A-levels altogether. She started doing Open University courses at almost 15, having done nothing formal up to then. In three and a half years (doing nothing like 30+ hours per week), she has gained the equivalent of 6 A-levels and it has cost almost nothing because OU courses are funded. The full story is on the home education exams website.
EHEers are great at sharing info about free and cheap things in the area. We started at our LA Saturday music school because an EHEer told us that you pay one family price and can attend as many classes as you can fit into the four hours it is open.
How do you make sure your child still mixes with other children?
Really, really not an issue! Church, kids' clubs, dance/music/drama/sports clubs, HE groups.
How did you convince your dh/dp if they weren't too sure?
Can't really comment. Mine didn't object but we have been divorced for a long time and he was not helpful with DS and late reading. To generalise, men seem to be less accepting of differences in learning than women. I'd point him in the direction of websites and books.
Any tips etc?
Don't worry! You have to work really hard to stop children educating themselves. Just do whatever seems good and fun now while your DC are so young and keep on doing it past the age of five - the children don't know that is supposed to mark a big change in learning style, so they keep on learning in the same way.
Have fun.