The distribution of renewable energy resources (RERs) is currently uneven and is largely influenced by their affordability across various communities. This has led to disparities in access to green energy for different community members. To address these inequalities, this study proposes an equity-oriented power-sharing mechanism that incorporates demand response (DR). The implementation of this approach will increase the availability of green energy for all members of the community in mixed neighborhoods. First, a DR program is introduced for conventional homes (i.e., homes without RERs) to maximize the consumption of RERs by shifting their load to RER excess intervals. Then, a proportionally fair mechanism is introduced to distribute the available resources among community members during times of high excess. The objective is to minimize the grid dependence of community members by reducing their reliance on purchasing power from the grid. To ensure renewable energy homes (i.e., homes with installed RERs) maintain their green energy access, additional constraints are put in place to prioritize their energy needs when compared to the non-sharing case. Three indices (green energy access, grid dependence, and cost reduction) are introduced to evaluate the performance of the proposed method in different cases: the base case, the power-sharing-only case, and the case of power-sharing with the DR. Finally, the impact of different seasons, day types, and user-defined parameters is analyzed. Simulations have shown that the proposed method can significantly increase the green energy access of conventional homes without affecting the access to green energy of renewable energy homes. It also decreases the grid dependence and the electricity cost of the entire community.