The hydromagnetic Kelvin‐Helmholtz instability has been extensively studied in simple plasma configurations, but more complex situations relevant for fusion research involving the combined role of effective gravity due to acceleration, velocity shear, density and magnetic field stratification has not yet been investigated for compressible plasmas. We consider an isothermal equilibrium configuration with stratified density and magnetic field in a compressible plasma. The dispersion relation can be reduced to a highly complicated algebraic equation that involves many parameters. Various cases are examined. Analytical conditions for stability are given for a stratified plasma with no density jump. When there is a density discontinuity, the conditions for the existence of unstable modes are presented. The limiting case without gravity is examined.