Lilli, I am not exactly the person to ask about companion plants for irises; apart from certain garden limitations here (drought, critters), my irises in-ground at the moment are rather scant. Also, my climate may not be similar to yours. That said...
Non-flowering
'Stachys' such as 'Helen von Stein'
can be a good companion for bearded irises, however you have to be diligent to keep it in bounds, and from smothering the irises. It always looks ratty during the winter, though, and needs a late winter/early spring cleanup.
I have a fair amount of
Iberis for spring bloom; those can be considered a companion of sorts, and they don't have the invasiveness problem that the
Stachys does. In back of the irises, or bordering the beds, you can always use various shrubs and sub-shrubs. Currently I have one
Euryops in an iris bed (with plans to add at least one more), and another bed (which I should be planting right now) will have some
Cuphea nearby. (In that bed the irises will be backed by some daylilies, which I hope will get enough sun to bloom; that bed is a part shade/part sun bed. I don't consider the daylilies to be "companions" though; they will be dormant daylilies and the foliage will be fresh and growing and green during iris season, but it will be too early for bloom. If the daylilies can't manage to bloom, then I will yank them out and replace them with either more
Cuphea or else perhaps dwarf azaleas.)
One thing that I have learned is to NOT put anything that needs frequent deadheading behind the irises, such that you have to tromp through the irises in order to deadhead them. I have 4 of the summer blooming
Verbena 'De La Mina' behind my yellow 'Luminosity', and I am going to yank them all this fall. (Apart from the deadheading issue, they are somewhat tender and almost died on me one winter.) I'm not sure whether or not to replace them with more
Euryops (which also need deadheading but only in the winter/spring, and their yellow blooms are so valuable then), or with some
Cuphea (which might fry in that afternoon sun location, backed by stone), or with some dwarf boxwood. (Come to think of it, I have some box in a small bed that I am reworking right now, which had/will have 'Darkside' and 'Afternoon Delight' in there. So yes, I guess box makes a good companion.)
(
Verbena lilacina 'De La Mina' might be a good companion for reblooming irises, but only if it is off to the side or where you don't have to tromp through the irises to deadhead it. Shown in the second image behind the iris 'Luminosity'.)
I took a quick look through my images, and I see that I forgot to mention
Osteospermum. I have some of that grown in one of the iris beds, and it can tolerate the sun and drought that the irises need, as well as provide companion bloom. It comes in different colors, so you can pick and choose to go with your iris color scheme.