Consumers with low socioeconomic status (SES) eat less healthy and sustainable diets than consumers with higher status. This is attributed, at least in part, to inequalities in health communication. An online survey with 134 socioeconomically disadvantaged consumers in Italy was conducted to test the effectiveness of tailor-made communication material (infographics) about healthy and sustainable eating (HSE). Participants were recruited at two social supermarkets by a social service organisation as well as via a crowdsourcing platform. Participants found information about HSE delivered through infographics moderately effective in increasing motivation, capability, and opportunity for HSE, and moderately useful and likely to impact their behaviour. Certain messages were more effective than others for native consumers, while migrants showed more indifferent responses to the various messages and manifested lower motivation to shift towards HSE, limited access to and seeking of nutrition-related information, and lower trust in information sources. Selecting which messages to deliver strategically, while also considering differences between segments of the target audience and their preferred sources and channels for communication, is promising; yet, structural changes related to food's affordability and availability are also needed to facilitate an effective communication.