We describe an instrument combining the advantages of two methods, axisymmetric drop shape analysis for well-deformed drops and capillary pressure tensiometry for spherical drops, both used for measuring the interfacial tension and interfacial rheological parameters. The rheological parameters are the complex interfacial elasticity, and the surface elasticity and viscosity of Kelvin-Voigt and Maxwell rheological models. The instrument is applicable for investigation of the effect of different types of surfactants (nonionic, ionic, proteins, and polymers) on the interfacial rheological properties both of air/water and oil/water interfaces, and of interfaces between liquids with equal mass densities. A piezodriven system and a specially designed interface unit, implemented in the instrument, ensure precise control for standard periodic waveforms of surface deformation (sine, square, triangle, and sawtooth) at a fixed frequency, or produce surface deformation at constant rate. The interface unit ensures accurate synchronization between the pressure measurement and the surface control, which is used for real-time data processing and feedback control of drop area in some of the applications.