Are there any colleges that offer admission to both MSC in Home Science and B.Ed programs together?

Yes, You can do M.Sc and B.Ed together. You can enroll in a regular full-time degree course and pursue another degree from the same university or another institution.

Here are some universities in India that offer integrated M.Sc and B.Ed programs: 

Cntral University of Rajasthan

Mohan lal Sukhadia Uni

Yes, You can pursue both courses as an integrated dual degree course. You can do M.Sc. In open university like IGNOU or YCMOU. And do B.Ed in regular college.Various colleges/universities offering integrated B.Ed+M.Sc are listed below:

1) BIT, Mesra
2) Yogi Vemana University
3) Kakatiya University
4) Na