First, prepare your jars and lids as per proper canning procedures.
Combine berries, cherries, and sugar in your preserving pot over medium heat. Add the lime juice, and cook for 30-40 minutes, stirring frequently, until the jam has reached its setting point. Remove from heat.
Using proper canning procedures, pour the finished jam into prepared jars leaving a 1/2 inch headspace. Remove any air bubbles with a chopstick or bubbler. Wipe the rims clean, apply the lids, and tighten the rings to finger-tip tightness. Process for 10 minutes in a water bath canner to seal.
Once processed, set the jars on a folded kitchen towel and let them rest undisturbed for 24 hours. Properly sealed jars will keep for up to one year in a cool dark place; any that have not sealed should be put in the fridge and eaten first.