(1) Background: Ongoing research indicates that it is reasonable to separate a company’s digital maturity assessment by relating it to organization and process levels. The lack of such models in the literature should be considered a research gap. This article aims to present a model framework for assessing enterprise digital maturity that considers two dimensions—organizational and process. The organizational dimension reflects the overall level of digital transformation and refers to the implemented concepts, solutions, and management tools covering the entire enterprise structure. The process dimension focuses on the level of operational divisions. (2) Methods: Analyses were conducted according to the developed research procedure, which included five steps. The research used the following methods: a critical literature analysis, an analysis of the obtained results and their synthesis for the formulated model, and verification and validation of the developed assessment tool and procedure in a selected enterprise based on interviews with managers and direct observations. (3) Results: Based on the literature review, eleven digital maturity areas of the model were defined, and five levels of assessment were formulated for each area. A diagnostic tool for enterprise self-assessment consisting of 105 questions was also developed. (4) Conclusions: The developed model was positively reviewed by the managers of the assessment team that audited the selected enterprise based on it.