Hi Gwen,
I'm not sure who you mean by 'Durham online'. Do you mean 'Durhamrecordsonline' ?
If so, the record would only be a transcription of their marriage details, which you already have.
The marriage allegation, is the application for the issue of a licence to marry. It normally contains the details of the couple, and confirmation of their eligibility to marry legally, which were given under oath. A third party (one or more named persons) is required to stand as bondsman in the sum of about £200, which is forfeited if the statements are found to be false. As far as I know, County Durham allegations are only held at Palace Green and would have been issued within 3 months prior to the marriage.
As far as I know, they are not searchable online yet. They are held in date order for each year so it would mean a manual search.
Regards,
Colin