Deployment of robots into hazardous environments typically involves a ``Human-Robot Teaming'' (HRT) paradigm, in which a human supervisor interacts with a remotely operating robot inside the hazardous zone. Situational Awareness (SA) is vital for enabling HRT, to support navigation, planning, and decision-making. This paper explores issues of higher-level ``semantic'' information and understanding in SA. In semi-autonomous, or variable-autonomy paradigms, different types of semantic information may be important, in different ways, for both the human operator and an autonomous agent controlling the robot. We propose a generalizable framework for acquiring and combining multiple modalities of semantic-level SA during remote deployments of mobile robots. We demonstrate the framework with an example application of search and rescue (SAR) in disaster response robotics. We propose a set of ``environment semantic indicators" that can reflect a variety of different types of semantic information, e.g. indicators of risk, or signs of human activity, as the robot encounters different scenes. Based on these indicators, we propose a metric to describe the overall situation of the environment called ``Situational Semantic Richness (SSR)". This metric combines multiple semantic indicators to summarise the overall situation. The SSR indicates if an information-rich and complex situation has been encountered, which may require advanced reasoning for robots and humans and hence the attention of the expert human operator. The framework is tested on a Jackal robot in a mock-up disaster response environment. Experimental results demonstrate that the proposed semantic indicators are sensitive to changes in different modalities of semantic information in different scenes, and the SSR metric reflects overall semantic changes in the situations encountered.