Bismihi ta'ala
If what you mean by "unmarried partner" is that you are both non-mahram to each other, then of course you cannot have physical contact, or show any form of affection, physical or verbal.
Going out together in this case would also be problematic, due to the feelings you would have towards each other. Unless you are a large group, or other such circumstances.
Otherwise, if it is just you two alone, then it is pretty much going out on a 'date'.
If you are both interested in marriage, then get married.
If not, hanging out and going to movies with a non-mahram is certainly something that you must avoid.
And Allah knows best.