RC for EEA spouse in Hungary - need health insurance?

[Elmart]

Hi everyone!
My husband (UK) and I (non-EU) just moved to Hungary, where he started a new job. I came here on Shengen "C" visa.
I am going to apply for Residence Card as non-EU spouse, so I called the immigration office to find out what documents I need.
Most of the requirements seem reasonable, but they said I need to buy a full cover health insurance for myself, which sounds costly.
My husband has his EHIC card and even received some kind of local helth number. I thought I might be entitled to join public health system here as his spouse? Or is it not the case?
What do you think, is it a legal requirement under EU law? Can I find a way out of this or gotta do what they say?
Will really appreciate any advice!