Place strawberries and rhubarb in medium-sized stockpot. Add 1½ cups of the sugar, stir into fruit, and let stand for 5 minutes. Place pot over medium high heat to bring mixture to a boil, stirring frequently. Boil hard for 4 minutes, starting the timing when the mixture reaches a rolling boil. Stir frequently.

Add the remaining 1½ cups of sugar, stirring to blend it in. Return mixture to a rolling boil, continuing to stir frequently to prevent it from scorching. Boil mixture briskly over medium-high heat for 4 minutes (starting the timing when the mixture reaches a rolling boil again), continuing to stir mixture often.

Remove jam from heat and stir in the lemon and orange juices. Skim off, and discard, any foam that remains. Jam will appear somewhat runny and watery but will thicken somewhat when set. Fill sterilized jars, leaving about 1” headroom to allow for product expansion when freezing. Apply heated lids and jar bands to jars. Let jars stand on counter for 24 hours, without disturbing, to allow the jam to set before freezing.