Your sentence, as is, would translate as :
Si les femmes mariées ne travaillent plus, le mari doit assumer davantage de responsabilités et gagner plus pour soutenir la famille, ce qui n'est pas favorable à votre relation à long terme.
"Which" translates as "ce qui".
Your sentence sounds awkward because you mix a plural (the married women) and a singular (the husband), then you follow with an address to the audience (your relationship).
I would rephrase it as :
If a married woman stops working, her husband bears a greater responsibility, since he needs to earn more in order to support the family. This works against their relationship on the long run.
In French, it would sound like :
Si une femme mariée arrête de travailler, son mari porte une responsabilité plus lourde puisqu'il doit gagner plus pour soutenir la famille. À long terme, cela porte préjudice à leur relation.
Bear in mind that you can often split a long sentence into shorter ones. This method can dispense you of building involved "which" structures.