ConvertUsing.cs

public static void Main(string[] args)
{
	Mapper.Initialize(x => {
  		x.CreateMap<To, From>()
        	.ReverseMap();
		x.CreateMap<string, Serialized>()
			.ConvertUsing(y => JsonConvert.DeserializeObject<Serialized>(y));
		x.CreateMap<Serialized, string>()
			.ConvertUsing(y => JsonConvert.SerializeObject(y));	
	});	
	Mapper.AssertConfigurationIsValid();
	
	var test = new From
	{
		Test = new Serialized
		{
			Min = 1.23,
			Max = 2.34
		}
	};
	
	var test2 = Mapper.Map<To>(test).Dump();	
	var test3 = Mapper.Map<From>(test2).Dump();
}

public class Serialized
{
    public double Min { get; set; }
    public double Max { get; set; }
}

public class From
{
    public Serialized Test { get; set; }
}

public class To
{
    public string Test { get; set; }
}