Cut pomegranates open and deseed. This may take a while, depending how skilled you are at deseeding pomegranates. Save arils and discard the peel.
Save a couple tablespoons of arils for later, place the rest in a blender, and pulse until the arils break down and you get a thick smoothie. Pour the juice through a strainer and make sure to strain really well, until no juice remains on the seeds. Discard seeds and pour juice in a large jar. Add the saved pomegranate arils.
Cut 2 oranges in half. Slice one half into thin slices and add orange slices to the jar with pomegranate juice. Squeeze juice out of the remaining halves, and add juice to jar.
Stir orange pomegranate juice well and taste. If it is too sour, add 2 ts of sugar and 1 cup water to dilute and stir to combine.