Can one creature or character use both an immediate interrupt and an opportunity attack in the same round, or are they mutually exclusive actions?
Yes. They can be performed during the same round and during the same turn.
An Opportunity Attack is defined as:
Thus an opportunity attack is an opportunity action which occurs once per enemy turn and interrupts their action on their turn.
This definition is reinforced by Opportunity Action:
Despite using the term "interrupts" it is no-where classified as an Immediate Action:
While there are two types of immediate action (immediate interrupt and immediate reaction) they are both triggered off the immediate action definition, rather than the opportunity action. As these two sub-types of actions (immedite interrupts versus opportunity attacks) are based on different actional definitions that restrict by rounds for IIs and turns for OAs, they're different and may be taken in the same round. If they happen from the same action, there is no clear ruling as what triggers first, and so it is by the choice of the person taking both actions. II triggers tend to be very precise, however, and will usually resolve the issue if read carefully.
The most pragmatic example is that of a spellcaster next to a warden. The caster provokes by casting a ranged attack at a different target, as well as violating the mark.
Warden's fury triggers on:
Whereas the OA triggers on:
As, pedantically speaking, the decision to use a power occurs before the targeting of the power, the warden would first resolve her OA, and would then resolve her II, severely castigating the artillery for being so foolish as to not shift first.