Cut bacon into 1/2-inch pieces and in a large heavy skillet cook over moderate heat stirring, until crisp and golden. With a slotted spoon transfer bacon to paper towels to drain.
Thinly slice cabbage and discard coarse stems from mustard greens. In a large rack set over boiling water steam cabbage, covered, until crisp-tender, about 10 minutes. Transfer cabbage to a large bowl and keep warm, covered. In a steamer rack set over boiling water steam mustard greens until tender, 10 to 15 minutes. Add mustard greens to cabbage and keep warm, covered.
Mince garlic. In a small saucepan heat garlic, butter, and oil until butter is just melted. Drizzle butter mixture over vegetables, tossing to distribute evenly, and season with salt and pepper.
Transfer vegetables to a serving dish and serve topped with bacon