My spouse and I agree on joint custody. Does that mean I have my children fifty percent of the time?

If the parties agree in detail on specific rights, duties, and possession terms, call it joint custody, and the court finds the agreements reasonable, then joint custody means whatever you and your spouse define it to mean.

Confusion reigns over what the court means by joint custody. The Courts do not define it to mean that each parent has the children fifty percent of the time. In fact, joint custody, called joint managing conservatorship by the courts, refers more to the rights and duties of parents than the physical possession of the children.
There are three sections in the Texas Family Code addressing rights and duties of parents: (1) rights that parents always have, (2) rights and duties that parents have during periods of possession, and (3) rights and duties that are shared between the parents (a joint managing conservatorship) or provided solely to one parent (a sole managing conservatorship). Most cases appoint the parties as joint managing conservators. Having one parent appointed sole managing conservator does not mean the other parent will not have visitation with the children.

The rights that may be shared in a joint managing conservatorship are the following: (1) the right to designate the primary residence of the child; (2) the right to consent to medical, dental, and surgical treatment involving invasive procedures, and to consent to psychiatric and psychological treatment; (3) the right to receive and give receipt for periodic payments for the support of the child and to hold or disburse these funds for the benefit of the child; (4) the right to represent the child in legal action and to make other decisions of substantial legal significance concerning the child; (5) the right to consent to marriage and to enlistment in the armed forces of the United States; (6) the right to make decisions concerning the child's education; (7) the right to the services and earnings of the child; and (8) except when a guardian of the child's estate or a guardian or attorney ad litem has been appointed for a child, the right to act as agent of the child n relation to the child's estate if the child's action is required by a state, the United States, or a foreign government.

Each of the above rights and duties may be given exclusively to one parent (for example, the right to designate the primary residence of the child is usually given exclusively to one parent, and that parent is often referred to as the primary joint managing conservator), independently shared by the two parents, shared by the two parents where the parents must discuss the issue but one parent has the ultimate decision, or shared by the parents where the parents must discuss the issue and agree on how to handle the issue.