Process assessment is a means to characterize a software process for improvements. The main result of an assessment is a set process profiles, which describes the gap between the assessed processes and reference processes. Based on assessment results and an organization's business goals, target process profiles are proposed, often with supplementary suggestions, regarding how the target profiles can be implemented in practice. We discuss an approach to enhance the three steps of an assessment with process models. In the approach the actual process profiles are illustrated by a descriptive process model, which is constructed by mapping the elements of the reference processes to the organization's process elements. The modeling counterpart for the target process profile is a generic target process model, where elements from the reference processes are added to the descriptive process model to fill the gap between the target and actual process profiles. To demonstrate the suggestions for improvements, the reference process elements in the generic target process model are replaced by elements from practical software engineering and management methods. A process library consisting of both the reference processes and a set of practical methods supports the construction of the process models.