Yes, you may! It depends upon the context.
The comment you are referring to from "The Big Bang Theory" is probably slang. If you can provide me a URL link to this episode on YouTube, I'll be glad to take a look at it and respond in more detail. (Note: Use of the term 'girlfriend' is vernacular English.) The word "girlfriend" (and "boyfriend") are broad concepts in spoken English today; much as the word "love" is used in modern culture.
Summary: It depends upon the context.
Meanings (in American culture):
1. "Girlfriend" usually means an exclusive dating relationship between lovers. (This refers to a "pre-engagement" type of dating relationship.) {Primary meaning.}
2. "Girlfriend" can also mean casual friendship. (This reference is used primarily between female roommates, classmates, office-mates, etc.) {Secondary meaning.}
3. Slang expressions using "girlfriend" are not uncommon. (Yet, slang expressions typically dilute the meaning of the word; or they are a parody of the word "girlfriend".) {Third meaning.}
4. "Girlfriend" may sometimes [rarely] be used between boys and girls who are strictly friends — in the Platonic sense. However, in this context: they would have been "best friends" from high school, or "friends of the family", or have become friends through marriage of a close friend, etc. (Note: The circumstances underlying the use of "girlfriend" in this context are unique, and exceptionally rare in American culture.) {Hybrid meaning.}
Hope this is helpful to you!
Sorry this is such a formal answer! :( Let me know if I can provide better clarity...
BTW: I'm an American (by birth). Native English speaker. Living in the USA. I work as a corporate trainer in computer engineering & architecture. ~ Pardon the fragments! ;) lol