Dear candidate,

No , you can either opt for a bachelor's degree in English Hons or in mass communication. There I no course as such that allows you to opt for mass communication as a minor subject along with English as th main subject . 

But  you can do diploma in mass communication along with English Hons .

OR

you can to do the two courses simultaneously. You can go in for regular B.A course. There are various institutes like R.K.Films and Media Academy in Delhi which offer weekend classes. You will need to balance your time for both the courses. Most of the cities will be offering similar courses. If you want to enter the field of Mass Communication then certainly go in for Post Graduation from MICA.

Hope the answer is helpful.

All the best!