As a featured smart-grid technology, demand response (DR) provides utility companies with unprecedented flexibility to improve the reliability of electricity service in future power systems. However, due to the uncertainties arising from the demand side, the extent to which DR can be utilized for capacity support poses a major question to the utilities. To address this issue, this paper proposes a new methodological framework to assess the potential reliability value of DR in smart grids. The framework is established on the concept of capacity credit (CC), and it accommodates different types of uncertainties (i.e., probabilistic and possibilistic) accrued from physical and anthropogenic factors in DR programs. The capability of DR during operation is considered as a synthesized result of multiple facets, i.e., users' load characteristics, participation levels, and load recoveries, and different models are developed to represent each component. To characterize the stochastic nature of demand responsiveness, the fuzzy theory is introduced, and possibilistic models are proposed to describe the human-related uncertainties under incomplete information. In addition, considering that in reality, DR operation could affect the comfort of customers, the dynamics of demand-side participation have also been incorporated in our study, in which two utility-based indices are defined to quantify the effect of such interdependency. Using a probabilistic propagation technique, the different types of uncertainties involved can be normalized and systematically addressed under the same framework. Then, the relevant models can be applied to the CC evaluation procedures, wherein two dispatching schemes (i.e., reliability-driven and coordinated management) are considered to study the effect of DR operation on its CC. The proposed methodology is tested on a modified RTS system, and the obtained results confirm its effectiveness.