High cost of nutritious foods and eating out of home (OH) might be barriers to healthy and sustainable diets. We examined adherence to Dietary Approaches to Stop Hypertension (DASH), EAT–Lancet reference diet (EAT) and Mediterranean diet score (MDS) and the associations with dietary cost and eating OH. We evaluated cross-sectional data from single multiple-pass 24-h diet recalls from 289 young adults (18–24 years) in Tirana, Albania. Dietary cost (in Albanian Lek (ALL)) was estimated by matching food consumption data with retail prices from local fast-food chains, supermarkets, restaurants and food vendors. Poisson regression was fitted to models that included DASH, EAT and MDS as dependent variables to assess associations between healthy sustainable diet indicators and dietary cost and eating OH. Adjusted models were controlled for BMI, sex and total energy intake (kJ) using the residual method. Our findings indicate relatively poor adherence to healthy and sustainable dietary patterns among young men and women in Albania. Furthermore, better adherence to DASH, EAT or MDS was not associated with dietary cost (per 100 ALL; range incidence rate ratios (IRR): 0·97–1·00; all (un-)adjusted P > 0·05). Nonetheless, eating OH was related to lower adherence to DASH (IRR: 0·79; P = 0·003) and MDS (IRR: 0·69; P < 0·001). In conclusion, adherence to health and sustainable dietary patterns was poor and not differentiated by cost, but rather source of foods (i.e. OH or at home). Further research on the potential public and environmental health effects of these findings is warranted in Albania.