While it's unreasonable to think married folks will never ever have crushes outside their sacred union, acting on them is a big-ass-no-no.
When does a crush turn from innocent to guilty? That is a demarcation every couple has to determine for themselves. Some women can't tolerate knowing that their man finds the Williams sisters sexy. Other women could care less if their man compliments her friend's butt shape in a pair of capris.
From what you're telling me, your man HAS decided his crush has crossed the line; not that he is sneaking into motels with this woman, but in that he deliberately and purposefully conceals their pics and text swaps. He feels this is an emotional betrayal to you; sinister, as you put it.
Now it's up to you, and there by both of you, to figure out what happens next. Have THE conversation. Does he need to tell you something you don't want to hear, but need to know? Or, maybe it's as simple as reminding him that the needs and feelings of those in this marriage come first, that his behavior is hurtful and troubling.
We know he's able to communicate with this woman, now let's see how he communicates with you.