We report on a compact interferometer for the water-window soft-x-ray range that is suitable for operation with laser-plasma sources. The interferometer consists of a single diffractive optical element that focuses impinging x rays to two focal spots. The light from these two secondary sources forms the interference pattern. The interferometer was operated with a liquid-nitrogen jet laser-plasma source at lambda=2.88 nm. Scalar wave-field propagation was used to simulate the interference pattern, showing good correspondence between theoretical and experimental results. The diffractive optical element can simultaneously be used as an imaging optic, and we demonstrate soft-x-ray microscopy with interferometric contrast enhancement of a phase object.