https://www.medievalists.net/2024/11/christians-muslims-first-crusade/?utm_source=gravitec&utm_medium=push&utm_campaign=Push%20Notification
Interesting read
Nicholas Morton's book "The Crusader States and their Neighbours: A Military History, 1099-1187" covers co-operation quite a bit (longer period than the 1st Crusade obviously).
https://www.amazon.co.uk/Crusader-States-their-Neighbours-1099-1187/dp/019887880X
He has also done a few short video talks which are interesting - https://www.youtube.com/@MedievalNearEast/videos