My bf and I bought a house in May 2018 - no kids together, but he has 2 dependents, and I have 1. We've both been Head of House in previous years, how should we file now?

[Hal_Al · Accepted solution]

If you didn't move in together until May, you can both file  HoH for 2018 as you both (probably) paid more than half the total yearly household expenses*, for your respective dependents, for 2018. 

However, going forward (2019+), only one of you can claim HoH. The other will have to file single. Getting married by 12-31-19 would allow you to file as Married Filing Jointly (MFJ).

*100% for 5 months + 50%(+/-) for 7 months = more than half of the year's total.

[Opus 17]

I would be careful about this.  I think @Hal_Al may be technically correct, but I would document everything.  How much your housing cost from January to May and how much you paid (and if any part was paid by relatives, govt support and so on) and how much your housing cost from May to December, and who paid what.  

Going forward, you have one household and only one person can pay more than half of your current household.

[Opus 17]

The one who pays more than half the total household expenses can still file HOH (it must be MORE than half, but $1 more is enough); the other files single.  You can't both be "head of household."