Relying on Random Utility Theory (RUT) as the guiding mechanism for the Data Generating Process (DGP), this paper uses households consumption choices on cooking fuel, drinking water, and sanitation from the 2014 United States Agency for International Development's (USAID) Demographic and Health Survey (DHS) data on Burkina Faso, to characterize and investigate the inter-linkages between health consciousness and environmental consciousness, and their relationship with wealth in a low income country context. We achieve this by specifying sequentially three econometric modeling frameworks: the first one being independent binary probit (IBP) models to describe each choice process, followed by a fully parametric trivariate probit (FPTP) model to account for choice dependency, and finally by a semi-parametric trivariate probit (SPTP) model to further relax the linearity assumption. Based on the Akaike Information criteria (AIC) and the estimated Trivariate model correlation coefficients, the SPTP framework is found to be the best specification for describing the observed consumption behaviors. The results show that increased wealth level raises households health and environmental consciousness, while leaving the relative preference ordering over the elements in the household consumption basket unchanged.