Prepare boiling water canner. Heat jars and lids in the dry cycle of your dishwasher until ready to use. (You can keep them in simmering water, but they are all wet as well as hot, if you go that route.).
Combine the lime peel with several cups of water and bring to a boil. Boil over Med-High heat for 5 minutes, until peel is softened. Drain and discard liquid. Return peel to pot.
Add strawberries, raspberries, and lime juice to the pot with the peel and mix well.
Gradually stir in the pectin.
Bring mixture to full roiling boil that can not be stirred down, over high heat, stirring constantly.
Add entire measure of sugar, stirring to dissolve. Return mixture to full boil. Boil hard for a full minute while stirring constantly. Remove from heat.
Ladle hot jam into hot jars, leaving 1/4 inch headspace.
Wipe rim and center the lid on the jar. Apply band until fit is fingertip tight. Do not over-tighten.
Process in a boiling water canner for 10 minutes.
Remove jars and cool. Check lids for a good seal in 24 hours.