Monte Carlo simulations are used to study adsorption of highly asymmetric diblock copolymers to a polymer-polymer interface, and the results compared to self-consistent field theory (SCFT) predictions. The simulation model used here is a bead-spring model that has been used previously to study equilibrium and kinetic properties of spherical micelles [J. A. Mysona et al., Phys. Rev. E 100, 012602 (2019)2470-004510.1103/PhysRevE.100.012602; Phys. Rev. E 100, 012603 (2019)10.1103/PhysRevE.100.012603; Phys. Rev. Lett. 123, 038003 (2019)10.1103/PhysRevLett.123.038003]. Interfacial copolymer concentration Γ and interfacial tension γ are measured as functions of bulk copolymer concentration at concentrations up to the critical micelle concentration over a range of values of the Flory-Huggins χ parameter. The dependence of interfacial pressure Π = γ_{0}-γ on Γ (where γ_{0} is the interfacial tension in the absence of copolymer) is found to be almost independent of χ and to be accurately predicted by SCFT. The bare interfacial tension γ_{0} and total interfacial tension γ(Γ) can also be accurately predicted by SCFT using an estimate of χ obtained from independent analysis of properties of symmetric diblock copolymer melts. SCFT predictions obtained with this estimate of χ do not, however, adequately describe the thermodynamics of the coexisting bulk copolymer solution, as a result of contraction of the strongly interacting core block of dissolved copolymers. Accurate predictions of the relationship between bulk and interfacial properties can thus only be obtained for this system by combining SCFT predictions of the interfacial equation of state with a fit to the measured equation of state for the bulk solution.