New analytical results are found for the capillary absorption of a liquid into a porous (sorptive) composite solid composed of n parallel layers of arbitrary thickness and material properties. The analysis is based on the `sharp wet front' model (also known as the the Green - Ampt model) and the results are exact for that model. A contact impedance acting at the interface between layers is included. The physical approximations of the model are discussed. The cumulative capillary absorption as a function of time is expressed in terms of the sorptivity, permeability and porosity of the materials of the individual layers. Experimental data obtained on composite bars of gypsum plaster and plaster/sand materials agree well with model predictions, although they test the model over only a limited range of parameter values. For these composite specimens, there is no evidence of a hydraulic contact impedance at the interface between layers. An asymptotic expression is given for the effective sorptivity of an alternating composite ABAB....