There are two types of custody to consider, Legal and physical.
There has been a tendency in the geographic region surrounding me (Greensboro / Winston-Salem) to give both parents legal custody unless there is some reason why it would not be in the child's best interest.
There is still a tendency to give the most physical custody (or time) to the parent that has been with the child the most.
In a lot of instances, the second parent will get every other weekend, (sometimes every weekend) and half holidays and some time in the summer.
The case will most likely start in mediation with a similar framework.
If the case fails in mediation, you may want an attorney for the court hearing.