We present phase diagrams for capillary condensation in chemically structured slit pores characterized by two first-order transitions from the confined "gas" over "liquid bridges" to "liquid." The split adsorption is produced by a complex periodic wall potential in one of the lateral directions that mimics inhomogeneities in real materials. After the previous condensation of liquid drops at the most attractive adsorption sites these may combine to form liquid bridges between opposite walls, separated between them by "gas gaps." Nonlocal density functional theory is employed to investigate this stepwise mechanism and the stability of the liquid bridges phase in function of the thermodynamic conditions and the pore structure, especially the ratio of the two typical lengths, the corrugation period lambda and the pore width H. Macroscopic predictions for the subcritical phase equilibria and the critical limit complete the study. The calculations confirm our previous results [P. Rocken and P. Tarazona, J. Chem. Phys. 105, 2034 (1996)] for an Ising lattice-gas model solved in the mean-field approximation.