"Free Church" is a loose label given to churches who separated or formed apart from the larger state churches of Christendom, generally stress an individual conversion experience and practice believer's baptism, and are often associated with one or more of the following movements: Anabaptism, Pietism, Restorationism, Pentecostalism, and Evangelicalism.

Mennonites.  The largest group directly descended from the radical wing of the 16th century reformation in Europe known as Anabaptists. The original Anabaptists rejected the notion that the church should be linked with the state and baptized believers upon their confession of faith. Today, the term "Anabaptist" is an umbrella term used to describe Mennonites, Amish, Hutterites, and some Brethren groups who trace their roots back to the original Anabaptist movement.  
Anabaptist Disabilities Network (ADNet) serves Mennonite and related groups with congregational resources for including persons with disabilities of all types.  ADNet is a member of MHS Alliance (Mennonite Health Services) which includes regional mental health centers and disability service providers. ADNet was the original creator of the Congregational Accessibility Network (CAN).

Baptists.  Baptists began as a free church movement in England, flourished in America, and now are represented around the world.  There are number of large Baptist groups in the USA and many smaller groups as well.  The following is a list of disabilities ministries within those groups.

American Baptist Church
American Baptist Home Mission Societies has resources for Ministering to Persons with Disabilities as well as a network of American Baptist Homes and Caring Ministries

Southern Baptist Convention (SBC)
The North American Mission Board of this largest Protestant denomination in the U.S. has a Disabilities Awareness program that includes a church survey tool. Their publishing ministry, Lifeway Christian Resources, has a Special Needs Ministry section.

Church of the Brethren. A peace church with roots in Anabaptism and Pietism.
Church of the Brethren Disabilities Ministry has an attractive website that includes a survey tool based on CAN's Congregational Assessment Survey.

Pentecostalism.  A movement within Christianity which emphasizes the direct work of the Holy Spirit in the life of the individual.  Various waves of Pentecostal revival since the early 20th century have produced a variety of denominations as well as a "charismatic movement" among Catholic and Protestant denominations.
See a review of a book Compel Them to Come In dealing with disabilities ministry in Pentecostal churches.  

Seventh Day Adventist (SDA) A restorationist church which grows out of a 19th century Adventist movement in the New England region of the U.S. 
The SDA North American Division has a Commission for People with Disabilities web page.