My wife and I would like to ask another couple to a group date at a local restaurant. I'm fine with this, but I'm unsure as to whether a "group date" implies that the check will be split between the two couples, or should we mention split checks to the other couple prior to the event?
I have a hard time imagining that the other couple won't assume a split check. I have never attended a group meal at a restaurant with the assumption that my meal will be paid for by someone else, outside of family relationships or explicit prior arrangement.
Assuming that this is in the U.S., your fellow couple would be at odds with customary behavior to just assume that you will pay for their meals. I mention this explicitly just because there probably are people out there that would assume so, but that's not the "normal" interpretation.
It's possible that phrasing might introduce some confusion about this, but that would be a rarer case:
My wife and I would like to take you two out for dinner!
It could also be the situation that, if other financial portions of the date are not split they might expect you to cover your share of the overall date by paying for the meal (maybe they are getting tickets for all four of you for a show, with the cost of your two tickets being roughly that of the meal, and haven't asked you for or discussed repayment). A situation like this should not be a surprise, and it would make sense to talk about the date's costs to eliminate any lack of clarity.
Mentioning split checks prior to the dinner would seem strange to me. If you are really uncertain, and dinner is the only expenditure, you could tactfully bring the subject up at the meal when ordering something for the table:
I think it would be nice if we got a bottle of wine. Should we go for [specific wine on the menu], and have them split that between checks?
Suppose you and your wife have booked into a really grand hotel in a city where a couple, who are old friends of yours live. If you say "Come and dine with us at our hotel", they will presume you are paying for all. If you say, let's meet for a meal in town, they will not.
I have been rebuked on this site for failing to backup my advice, because this site apparently does not deal in advice. All I can say is: this really happened, and I paid for an expensive meal for four.
You should make payment arrangements clear before you go out for dinner. It will be jarring for them if they think you are paying for them and then find out you are not, and can lead to hurt feelings.
So, if you are planning on them paying, when inviting them, say something like this:
Wife and I would like to go out to dinner with you on day at restaurant. We can only pay for ourselves, but we would really like you to join us.
If you are planning on paying, the initial wording is a bit different, as well as the second sentence:
Wife and I would like to take you out for dinner on day at restaurant. We will pay and would really like you to join us.