Bring boiling-water canner, half-full with water, to simmer. Wash jars (7 each 8-ounce canning jars) and screw bands in hot, soapy water; rinse with warm water. Pour boiling water over flat lids in saucepan off the heat. Let stand in hot water until ready to use. Drain well before filling.
Stem and crush strawberries thoroughly, one layer at a time. Mash banana thoroughly. Mix strawberries and banana. Measure exactly 3-1/2 cups prepared fruit into 6- or 8-quart saucepot. Stir in lemon juice.
Stir sugar thoroughly into fruit in saucepot. Add butter to reduce foaming, if desired. Bring mixture to full rolling boil (a boil that doesn't stop bubbling when stirred) on high heat, stirring constantly.
Stir in pectin quickly. Return to full rolling boil and boil exactly 1 minute, stirring constantly. Remove from heat. Skim off any foam with metal spoon.
Ladle quickly into prepared jars, filling to within 1/4 inch of tops. Wipe jar rims and threads. Cover with two-piece lids. Screw bands tightly. Place jars on elevated rack in canner. Lower rack into canner. Water must cover jars by 1 to 2 inches; add boiling water if needed. Cover; bring water to gentle boil. Process 10 minutes. Remove jars and place upright on a towel to cool completely. After jars cool, check seals by pressing middle of lid with finger. (If lid springs back, lid is not sealed and refrigeration is necessary.).