For both films: The ending credits suite's Crowning Music of Awesome is, in fact, a triumphant fanfare of Rick and Evy's love theme.
When Evy is genuinely upset about the way the scholars keep rejecting her application, despite her extensive knowledge and passion for her work, Jonathan immediately softens and stop teasing her: "You'll always have me, old mum." Complete with the sibling version of a Headbutt of Love.
Coward he may be, but Jonathan doesn't hesitate running to his sister's aid for a second.
Benny: You never believed in the legends. So why are you going back?
Rick: ... You see that girl? She saved my neck.
Rick gives Evy an archaeology kit that he swiped from the rival archaeologist, Burns. Made especially touching because it's probably her first kit, if not a replacement for the first one she lost when the boat sunk. Also the preceding dialogue where he appears to be working himself up to giving it to her.
Rick: So, uh, what are these old, uh, mirrors for?
Evy:Ancient mirrors. It's an ancient Egyptian trick, you'll see.
Rick: ...Oh. Uh, here, this is for you.
Evy: (vaguely confused look as she takes it)
Rick: Go ahead, it's, uh, something I borrowed from our American brethren, I thought you might like it- you might need it. You know, for when we're down, um (gestures a chiselling motion) Yeah. (walks away and sees the prison warden watching them, and immediately turns defensive) What are you looking at?!
Warden: (holds hands up in a surrendering gesture)
And another Rick telling Beni to get out of Evy's seat (which, by the way, is right between him and Jonathan).
Evy: (walking up to the group) Look what I found!
Rick: (instant Death Glare in Beni's direction] You're in her seat.
Rick and a completely hammered Evy have a conversation by the campfire during their first night in Hamunaptra, when she tells him enthusiastically about her parents and her lineage. You can just hear how passionate and proud she is, and how much she must have loved her parents.
When Evy furiously states that she is proud to be her parents' daughter, and of who and what she is, Rick just smiles with complete acceptance.
Jonathan: Well, I guess we go home empty-handed... again.
Rick: (looking at Evy) I wouldn't say that.
(Evy looks up at him, smiling in disbelief, and cue the music swell and Big Damn Kiss)
Jonathan had to go and be a party pooper.
The Mummy Returns
A very brief but meaningful moment between Jonathan and Ardeth. Things are looking bad for Ardeth, one of the mooks sneaks up behind him and almost offs him. Jonathan manages to pop the baddie off from a distance, Ardeth then gives him a silent nod of thanks. A few mintunes before Ardeth was insulting Jonathan's ability to kill anything. Very nice moment.
"Would you like to know what Heaven looks like?" "Later."
Novel version: "Nah. Hell, I already know."
Also from the novel, Rick and Evy's relationship mixes with Tear Jerker, as after Anck-su-namun leaves him to die, Imhotep looks up at them and with a ghost of a smile, acknowledges their love is much stronger than his and Anck's ever was.
While Imhotep was the one responsible for nearly killing Alex's family, he is the only one that is actually somewhat friendly to him. He stopped a couple of mooks from shooting Alex and defending Alex from Loc-Nah, as well as in his own way apologizing before sending a waterwave after them.
That last bit was more like a half-hearted/mocking apology. But he did seem genuinely happy for Rick and Evy, a truly faithful couple just before he died for good.
Rick jumps a goddamn bridge to try and save his son.
Rick and Alex, after Rick's just run across the jungle to save his son's life.
Rick: You know (pant) it's not (pant) easy being a (pant) dad.
Alex: Yeah. But you do it really good.
Rick to Evy: "You know, you and Alex are the only thing in the world that matter to me."
After Ardeth loses his pet bird, Horus. He wants to try to get to the rest of the Medjai on foot. However all it took for him to stay with the group was Rick practically begging him to help him find his son. During the skirmish between Rick's group, Imhotep's group and the Pygmies, just when Loc Nah was ready to do the killing blow on Alex, who better to rescue Alex and kill Loc Nah than Ardeth rushing in. His loyalty to his friends has grown a lot stronger than his loyalty to his fellow Medjai.