Remove the hard stem from the top of the figs and discard. Chop each fig in half.
Wash enough jars to hold 64 ounces of jam in hot soapy water (or in the dishwasher) and rinse well. Set aside. The number of jars will depend on the size of your jars.
Combine figs, strawberries, sugar, honey, balsamic vinegar, red wine (or apple cider) vinegar, water, lemons and thyme in a large saucepan over medium heat. (The larger, the better as the jam will sputter a bit as it thickens.)
Bring to a boil then reduce to a steady, rolling simmer. Cook for 10 minutes, stirring occasionally.
Discard the thyme sprigs and remove the lemon wedges..
Pulse/blend the jam with an immersion (or regular) blender until large pieces are gone but the jam still has a bit of texture. (Use the pulse setting if using a regular blender but allow the jam to cool down a bit and make sure the top of your blender container is vented to prevent a pressure build up.)
Cook on medium heat, partially covered (the jam will sputter at this point, as it cooks) for another 10 minutes or until the jam is thickened almost to the desired state. (It will get a bit thicker as it cools).
Taste the jam. If you would like it a bit tangier, add more balsamic vinegar, to taste.
Transfer to jars with tight-fitting lids. (Another option is to let the jam cool down in the pot so you can determine if it’s thick enough. Once it’s cool, if you’d prefer it a little thicker, just cook it a little longer. On the other hand, if it’s too thick, you can add more water (a tablespoon at a time) until your desired consistency is reached.)
Refrigerate for 2-3 weeks or freeze for up to a year.