Wash and stem the bell peppers and the jalapeno. Use a food processor to finely mince the peppers - be careful not to turn them into mush. You want the pieces of the pepper to be the consistency of a relish.
Put the minced peppers in a large bowl and combine with the canning salt. Let this mixture sit, covered, at room temperature for 3 hours.
Line a counter with lots of paper towels - I usually use 5 layers. You are going to be placing the drained peppers on these paper towels, so make sure you cover a large enough space; at least 1 foot by 1 1/2 feet.
Drain the peppers well in a colander, and then with your hands, which you have just washed in hot water with soap, squeeze the remaining moisture out of the peppers. You will see that a lot of water still comes out. Place the drained and squeezed peppers on the paper towels.
Make a spice bag out of a double layer of cheesecloth, and tie the allspice up in it.
In a non-reactive 10 to 12 quart pan, combine the drained peppers, the spice bag containing the allspice, the sugar, and the vinegar. Bring to a boil over high heat, then lower the heat to medium.
Cook the relish over medium heat for 1 hour, stirring frequently. Keep your eye on it - I have had this relish burn on me due to the high sugar content, so stir frequently - do not walk away from it. If the relish looks like it may be about to burn, turn down the heat.
When the relish is done, the pieces of pepper will be translucent and the syrup will be thick.
Remove the spice bag and ladle the relish into canning jars, leaving 1/2" headspace. Use a chopstick or other thin, non-metal utensil to run around the sides of the jar to make sure there are no air bubbles left in the jar. Wipe the rims of the jars with damp paper towels to remove any relish which got on the rims or the threads. Place the lids and the bands on the jars, just tightening the bands fingertip tight.
Process in a boiling water bath for 10 minutes, then remove and let sit, undisturbed, for at least 12 hours before checking seals. It is important to let them sit undisturbed for 12 hours because the sealing compound on the lids is still cooling and hardening, completing the seal. While the jars cool, you will hear a "plink" type sound from each jar - this is the jars completing the vacuum seal as the final air escapes the jar. After 12 hours have passed, remove the bands and check the lids - press down in the center of the lid. If you cannot push the lid down any further, the jar is sealed. If the lid "gives" a bit, and you can push it down, the jar did not seal. You can either put the band back on the jar, and reprocess it for another 10 minutes, or you can just put it in the fridge and use it within 3 months.