Why not just add some questions to the household nutrition survey about food security to make the links?
Such questions, if well chosen, can indeed show statistical relationships between nutritional status of children and household food security. Choosing the right food security indicators, however, can be difficult. Some common indicators are not always used appropriately (e.g. “food stocks in the household” is not an appropriate indicator where the household economy is heavily based on income and food purchases), while others are very difficult to collect accurately in a short questionnaire (e.g. income levels). Questions around household wealth, probably related to asset holdings, are probably the easiest to include in a nutrition survey. A more qualitative type of HEA would add value by (a) indicating the most relevant questions to include in the survey, and (b) providing more contextual information that would allow statistical relationships between nutrition and food security or wealth to be explained rather than just described.