The subject 'I' is a little strange - it would make more sense to say 'We' (as in you and your partner). You and your partner are a couple, and you dine out with another couple.
As for the tense, both are correct.
'We have been dining out..' refers to a recent period of time up until now. It means that you have dined out regularly with this other couple over the last few months. The implication is that this arrangement may be about to finish. Maybe you won't dine out with them again.
'We are dining out..' describes a continuing arrangement during this period of time. You have dined out regularly with this other couple over the last few months, and you expect to do the same this month and probably next month also.