Raising and caring for a child with ASD is a challenge for the parents’ marriage relationship. Caring for a disabled child changes the functioning of the family and requires greater involvement in care and specialist therapy. The respondents’ answers show that such parents experience higher levels of stress related to the upbringing and future of the child. However, parenting challenges need not be a negative experience if the parents support each other. The process of bringing up children in the family are related, inter alia, to the quality of their parents ‘marriage, which is influenced by the partners’ personal resources. The resilience of the partners and coping with this situation contribute to marital satisfaction. The aim of the study is to find out about the relationship between spouses’ resilience and coping styles and their assessment of marriage satisfaction. In total, 50 married couples participated in the study—50 mothers of children with ASD and 50 fathers, the partners of these mothers (N = 100). The following tools were used: the Resilience Scale (SPP-25), the Coping Inventory for Stressful Situations (CISS) and the Well-Matched Marriage Questionnaire (KDM-2), as well as a survey questionnaire (data on respondents). The results show that the gender of the parent of a child with ASD does not differentiate the overall assessment of the quality of marriage (the overall score on the scale indicates a low level of satisfaction with the relationship). When analyzing in detail the dimensions of individual scales of satisfaction with the relationship, one statistically significant difference was noted for the sex of the respondents in the disappointment dimension, showing that the level of disappointment in the quality of the relationship is higher in wives than in husbands. In the other dimensions of satisfaction with marriage: intimacy, personal fulfillment, similarity, there were no statistically significant differences in terms of gender of the respondents. The resilience of the spouses positively correlates with their assessment of marriage satisfaction, and in particular, openness, perseverance and determination to act increase the level of Task-oriented coping (SSZ) with difficult situations. All resilience factors negatively correlate with the emotional coping style (SSE). In both the studied groups, openness is a significant predictor of intimacy, and persistence is a predictor of self-fulfilment in a relationship. A predictor of disappointment in women is managing using substitute activities (ACZ), while in men it is the Emotion-oriented coping (SSE) style. The results indicate the need to support married couples raising a child with ASD during the pandemic.