Had same problem, what I did was copy the following line to the bottom of the "interface JQueryPromise extends JQueryGenericPromise" block.
/**
* Add handlers to be called when the Deferred object is resolved, rejected, or still in progress.
*
* @param doneFilter A function that is called when the Deferred is resolved.
* @param failFilter An optional function that is called when the Deferred is rejected.
*/
then<U>(doneFilter: (value?: T, ...values: any[]) => U|JQueryPromise<U>, failFilter?: (...reasons: any[]) => any, progressFilter?: (...progression: any[]) => any): JQueryPromise<U>;
/**
* Add handlers to be called when the Deferred object is resolved, rejected, or still in progress.
*
* @param doneFilter A function that is called when the Deferred is resolved.
* @param failFilter An optional function that is called when the Deferred is rejected.
*/
then(doneFilter: (value?: T, ...values: any[]) => void, failFilter?: (...reasons: any[]) => any, progressFilter?: (...progression: any[]) => any): JQueryPromise<void>;