The secret is balsamic vinegar, which not only acts as a preservative (in the unlikely event we ever have to worry about keeping this from spoiling) but bestows a zingy tart flavor to the fruit.
We used two cups of blueberries and raspberries, some fresh and some frozen. We then added half a cup of sugar and a tablespoon of balsamic vinegar. Basically, over a period of a couple hours I occasionally zapped it in the microwave for 5 minutes or so, then let it sit for a while. Ours reached an acceptable consistency after about five of these sessions. (Other online recipes I saw have you do it for longer periods, but since we have a small microwave we just set our own rules and this seemed to work OK.)
We also tried an earlier batch of this jam in PBJ cookies and found we liked them better because there was actual fruit bits in the cookie. (However, this batch of cookies was also made with whole wheat flour, so that may have been a variable as well.)