English does not have a formal word for "you".

This is one of many things that English doesn't share with other languages. 

I've spoken with one of my foreign friends about this and it took him a long time to get used to.

I've haven't thought much about this for English. I don't know if there is a word or phrase for what your asking. The closest thing I can think of is asking your friend to call you by your first name rather than the more formal Mrs "last name". Or say something about having a relaxed conversation.

I know in the US military if an officer wants a soldier to speak less formally he asks him to speak "freely", but that would be an awkward exchange to have if you aren't in the military.