Parental asthma or allergy have been linked to higher risk of asthma in a child; this occurs to a variable extent in different study populations. Moreover, it is debated whether maternal more so than paternal asthma history is a stronger predisposing factor: while in some countries/populations the maternal effect was clearly seen over paternal, in others the parental effects were equivalent, and in a few studies paternal effect dominated. Here we aimed to determine parental asthma and allergy effect in the Danish GEneral SUburban population Study (GESUS). This cross-sectional study has involved 21,362 adults aged 20+ years in the suburbs of Copenhagen. We used a combination of questionnaire approach, history of prescribed asthma medications and pulmonary function testing to determine odds ratios for maternal and paternal (and combined) asthma and allergy linked to asthma in the test subjects. We found that the input of maternal vs. paternal asthma effect was approximately equal (age and sex-adjusted OR 2.46, 95% CI: 2.15–2.81 for asthmatic mothers vs. 2.97, 2.58–3.42 for asthmatic fathers), except for the “ever asthma” age and sex-adjusted odds ratios where paternal allergy seems to have conferred a marginally greater effect (age and sex-adj. OR 1.96 for maternal allergy vs. 2.44 for paternal allergy, p = 0.03). Stratifying for gestational tobacco smoking did not affect the maternal results. We conclude that in the GESUS study parental asthma or allergy were strongly linked to higher asthma risk in offspring, without a prominent maternal or paternal effect.