We are using Authorize.net and on their site it says they accept electronic checks. How do I set up my Civi contribution page to accept both credit card and electronic check?
The default Authorize.net payment processor that ships with CiviCRM Core does not have the ability to handle e-cheques; try install:
do give it a good test - on a development/staging environment (with a copy of your site) - as it does not look like many people are using it;
current usage: 8
There is an extension that sets up the eCheck processor for AuthorizeNet. Once installed you should be able setup a separate processor for echecks.
More info in the link in KatinG's answer. This can be installed directly through CiviCRM (Administer>System Settings>Extensions Add New). We had a site using it under 4.6 with WordPress with no issues.
Hope this helps.