Based on the existing forms of interaction between expert systems in evaluating labor market competencies, this research aims to conceptually describe the functioning of a neural network system for assessing new competencies (using a multilayer network with Adaline neurons) in the labor market through a graphical model. The system’s functioning is shown as a process using the BPMN 2.0 process modeling language. The proposed scheme highlights the interaction between labor market actors (employers) and educational organizations in Russia. The research also proposes a fundamental scheme for integrating expert councils of educational organizations into data mining processes, labor market competency assessment, and enhancing the accuracy of the proposed neural network system. The functioning of the neural network system is described within three modules: data mining, communication-driven, and document-driven modules. The model identifies three top-level processes and nine subprocesses. Each subprocess is provided with documentary and informational support. The role of decision-making components (university expert councils) is described as a link in the neural human–machine assessment system. The process of developing relevant educational programs based on the evaluation of data collected through data mining is outlined. This research formulates a fundamental scheme for the interaction between employers (labor market actors), university expert councils, and federal authorities within a unified information space. The authors propose a concept for developing educational programs using neural network IT. A business process for forming educational programs is developed as a graphical model, displaying actors, support, top and lower-level processes, and connections.