The answer for Measles-mumps-rubella
The best source I know is the U.S. Centers for Disease Control and Prevention (CDC). Their
Advisory Committee on Immunization Practices (ACIP) says:
Measles-mumps-rubella (MMR) vaccine is not contraindicated for the close contacts of immunocompromised persons.
The answer for varicella (chicken pox)
In the same report, ACIP advises against giving certain other vaccines (e.g., the polio vaccine and the live flu virus) to someone in close contact with an immunocompromised patient, which implies that they think it's safe to give the varicella (chicken pox) vaccine to people in close contact with immunocompromised patients. But they don't explicitly say so.
Luckily, we can find the answer elsewhere...
The CDC's
General Recommendations on Immunization (part of the so-called
Pink Book) explicitly states that
MMR, varicella, rotavirus, and LAIV vaccines may be given when an immunosuppressed person lives in the same house.
There's further confirmation in the CDC's
Guide to Vaccine Contraindications and Precautions, which on Page 4 indicates that the varicella immunization is safe to give someone in close contact with an immunocompromised patient.
I suggest double-checking by phoning your hematologist's office. I remember asking my wife's hematologist about who in the family should get flu shots when she was on immunosuppressants (answer: everyone but my wife). That's the advice we had already heard, but getting direct approval from the doctor was reassuring.