Using a paring knife, remove the peel and pith from the grapefruits, navel oranges, and 2½ blood oranges. Thinly slice the peeled citrus fruit and set aside. (Cut any large rounds in half if desired.)
Squeeze the juice from the remaining blood orange half into a small bowl.
Add the mustard, honey, and vinegar to the blood orange juice and whisk until combined. Slowly add the olive oil in a steady stream and whisk until thickened. Season with salt and pepper to taste.
Halve, peel, pit, and slice the avocado.
Arrange the grapefruit, oranges, avocado, and greens on a serving platter or in a serving bowl. Drizzle with the vinaigrette, and serve immediately.