You are very sensible to be concerned but the answer will depend on a number of things.
Shingles is caused by the chicken pox virus, varicella zoster [VZV]. Most of us are exposed to VZV as children and this is when we develop chicken pox. Some people can't remember having chicken pox as they had it so mildly. The virus never goes away but lies asleep in the nerves. Later, for reasons we don't understand, it can wake up and travel down the nerves to the skin to cause shingles. There is live virus in the fluid in the blisters caused by the shingles and it can be infectious until all the blisters have crusted over.
If you have had chicken pox there is nothing to worry about, as you are immune to this virus causing your husband's shingles. Your husband can only give this virus to someone who hasn't had it - usually children, or sometimes the small number of adults who haven't had chickenpox before. If this person is very vulnerable to infection, such as after a bone marrow transplant, or if they are on steroid tablets, then the infection can be very serious.
If you have never had chickenpox, or if you are not sure whether you have had chicken pox, then you should call your transplant centre and discuss it with them They should have tested you to see if you are immune to VZV before your transplant. If you are not immune, or they are not sure, they will take a blood sample to check your immunity and then give you an injection of antibody to the virus.
Your risk of serious VZV infection gets less the further you go from your transplant and the fewer medicines you take to damp down your immune system (drugs like cyclosporin or steroids). In your case 3 months is still early and this exposure should be taken seriously.

