However, regardless of where the mortgage payments come from, whether you own the house as a "joint tenant" or as a "tenant in common" has a bearing.
If you own it as a joint tenant you do not own a discreet half of the property. It is owned jointly by the partnership (you and your mother). If anything happens to her the entire property reverts to you (your mother cannot leave "her half" to anybody else as she does not have a discreet half to leave. This also would be unaffected if she died without leaving a will.
However, if you are tenants in common you each own your own half. Mum can do what she likes with hers (and it will be subject to the rules of intestacy should she die without a will) and your husband may have a claim on your half as suggested by hc.
You may be lucky if your question is seen by either Barmaid or Buenchico who have more knowledge in these matters. But you really need to get a solicitor to investigate and formalise these arrangements for you, particularly as your husband has seemingly contributed a fair whack towards the house.