My used bike came with different front and rear tires. It appears to have some kind of Kenda commuter tire in the front, and Continental Country Ride in the rear. They are both the same size (700x28).
Is this perfectly acceptable or should a bike always have matching models (and/or size)?
My main concerns from mismatching tires:
It's perfectly okay to run different sizes, brands, and types of tires on the front and rear. As you note, rears will wear faster due to carrying more of the load. The grip threshold is largely irrelevant, since the front and rear will be exposed to different forces and grip requirements.
The main concern is keeping within the range of a single tube size if possible, since otherwise you'd need to have twice the spares on hand.
At the extreme end, there are 69er and 96er mountain bikes that mix and match 29" (622) and 26" (559) wheels on the same bike as well as Terry women's bikes with 24" (520) front wheels and 700c (622) rear. By necessity those run very different tires front and rear.
Yep, basically no problem mixing tire types, widths, and even diameters. The rear tire will carry more weight and generally wear faster, so that may be a consideration in picking different tires.
The front and rear are exposed to vastly different forces and there may be good reasons for having different tires as a result. On the front a narrow tire with light tread will permit turning with less effort, but on the back this isn't as much of a concern. OTOH, the front tire provides about 3/4ths of your braking ability, so that's an argument for giving it a more substantial (or at least not worn out) tread. In terms of sideways skids on slick/loose surfaces, a front tire skid is likely to result in a more out-of-control situation (ie, more road rash) than a rear tire skid, but it's harder to get the front skidding in the first place, so hard to say how tire style would affect this.
And (probably due mostly to the weight difference), punctures occur in rear tires 2-4 times more often than in front tires.
Of course, on a used bike the tires are apt to be different simply because they were not replaced in pairs. I'd generally say this is of no concern so long as they are roughly equivalent. If the front tire is much "heavier" than the back, though, my inclination would be to swap them.
As noted you do the braking on the front wheel, particularly if really braking when your centre of gravity moves forward over the front wheel. Therefore, if you are going to have odd tyres, put the wider one up front. This will give you better braking and cornering.
Tread matters little on-road for grip, even in the wet as bicycle tyres do not aquaplane. The main point of tread on a road tyre is to indicate wear. Too worn and the 'canvas' wears through and you get punctures.
Odd tyres are to be expected, the back wears out quicker for mysterious reasons for which the physics has as yet to be disclosed on B-SE, therefore you should end up with odd tyres - if you don't then you are not riding hard enough.
