Hi, in cases such as this one where on screen it's first a frame with "Die Hard", then a new frame with "With a Vengeance", and never the two together, the standard is to insert the colon. That's why the original title (based on the on-screen title) is listed as Die Hard: With a Vengeance on IMDb and also why we use that title here. I hope this makes sense. Thanks.

Here is the official website where you can see that the colon is officially part of the title.

@superboy97 said:

Here is the official website where you can see that the colon is officially part of the title.

So both criteria supports the decision. All good. Closing topic.