The temperature-dependent current-voltage and capacitance-voltage characteristics of interfaces between InP and a polypyrrole-phosphomolybdate hybrid material (PMH) are reported as a function of the redox potential, E-PMH, of the PMH (as controlled by its extent of oxidation or p-type doping level). The current-voltage characteristics of the interfaces are sensitive to EPMH and can be controlled over a much wider range than possible with analogous InP\metal interfaces. For the n-InP\PMH interfaces, the ability to tune the current-voltage characteristics by controlling E-PMH stems from control over the interfacial potential barrier phi(b) characteristically present at semiconductor interfaces. The spatially averaged phi(b) from capacitance-voltage measurements shifts from 0.59 to 1.05 V with a shift in E-PMH from -0.05 to +0.99 V vs SCE, leading to an index of interface behavior of S = dphib/dE(PMH) = 0.39. For the n-InP\PMH interfaces, heterogeneous electron transfer is slower than at the semiconductor\metal interfaces: the transmission coefficient kappa, describing the probability that a carrier with sufficient thermal energy to surmount Oh will actually cross the interface, is observed to be 0.003, independent of E-PMH and less than the semiconductor\metal limit of kappa = 1. For the p-InP\PMH interfaces, the extent to which the current-voltage characteristics can be controlled through manipulation of E-PMH depends on both phi(b) and kappa. The S value for the p-InP interfaces is nearly identical with that for the n-InP\PMH interfaces: the spatially averaged capacitance-voltage phi(b) shifts front 0.83 to 0.49 V with a shift of EPMH from -0.07 to +0.65 V vs SCE, leading to S = 0.37. Over the same range of E-PMH, the value of kappa decreases from the range of 1-0.1 to the range 0.05-0.0001 as E-PMH increases, suggesting that the majority carrier transfer rate depends on the details of the electronic structure of the PMH. The S values and empirical ideality factors observed for both the n-InP and p-InP interfaces are inconsistent with classic interface state models describing Fermi-level pinning. Nearly all of the interfaces demonstrate characteristic signatures of a heterogeneous barrier potential, such as, (1) ideality factors greater than unity and a decreasing function of temperature and (2) disagreement between the phi(b) extracted front capacitance-voltage and temperature-dependent current-voltage measurements (Richardson plots). The quantitative application of Tung's barrier inhomogeneity model and the influence of heterogeneity on the extraction of kappa and phi(b) are discussed.