Not a teacher.
I am not sure whether such term exists or not. However, In my place(though I am in India, I don't speak Hindi. As the author rightly pointer out, my state's language is different), People who don't speak English properly and mix Tamil(my mother tongue)with it, are usually referred as people speaking tanglish. I think the word tanglish would have evolved from "Tamil+English". It is a kind of mock if you say "he speaks tanglish". It is just to mean that he doesn't speak english properly. I guess the word "Hinglish" would also be meant in the same way.
(I don't know whether terms like this exist in other non-English-native countries. The reason why such terms are used in India may be because of the fact that English is considered as an indicator of one's knowledge. Speaking english is considered as kind as elitism here. I know a lot of parents who want to join their kids to School, have the first priority that their kid should speak English fluently. However knowledgeable a person may be, lack of fluency in English is always regarded as great deficient to him. I presume that's why those terms are used here )