"I am married to Josue" is the correct way to say this.

hi !!! I think both of them is correct but different way of using like I'm married to ( name) and I'm married with him/her you can also say we're married or (name) and I are married just think the logic of your sentence because sometimes some sentences is weird but it is correct and some sentences that we think it's correct well, its not have a nice day !!!