There is really no mandatory requirement from UKBA to submit an employment contract.
That is just one example of the many possible documents of evidence that you may choose to be used to support the financial aspects of the application.
If the employer can easily agree to a simple statement in letter format, that would also do the same job. Just indicating the date the employee started, job position held, pay details etc
The objective is to prove that the financial requirements needed by the UKBA can indeed be proven.
It's always up to the applicant and sponsor to decide how to comply and which specific documents are best to support their own individual circumstances.
If you have no reason or need to send the employment contract then why do it.
Concerning the bank statements, if you husband does not receive bank statements through the post he should be able to walk into the branch and request 6 months statements be printed off there and then and stamped. If the bank refuses he should speak with the manager. If all fails he should just place an order the past 6 months statements to be sent to him and pay any fees needed.
Obtaining banks statements is always possible.
Hope this helps you