Butterfly (also called Dolphin) and breaststroke are so called short-axis strokes. They both work from a pivot point in the hips and create an undulating motion forward. The major distinction between the two strokes is the arm recovery. Butterfly recovers above the water as you can see from the video below and breaststroke recovers right at the surface (usually in higher speeds, breaking the surface of the water).
The true butterfly uses an undulating dolphin kick and breaststroke a whip or frog kick as shown below. Rhythm and timing are two of the most challenging aspects of short-axis strokes. A good undulating motion is critical for being efficient with these two strokes. Since these two swimming strokes are quite similar and have a lot in common, it is not as hard to combine them together, however, the result speed of the stroke is very slow, hence butterfrog should not be used in competitions.
Watch carefully how the legs complement the arms in this video.
How about trying it the opposite way? Breaststroke arms and butterfly legs. This is actually a very common breaststroke drill which teaches you a nice body undulation and let's you strengthen your arms, especially if performed with paddles.