Normally Unity put Spine character in the "Default" sorting layer (Because it is a MeshRenderer) which will be hard to manage when used with other SpriteRenderer. You will be forced to move the Default layer around to sort them since the sorting layer is prioritised over Z transform value.

With this script you will have the two box normally seen on SpriteRenderer exposed on your MeshRenderer. (These 2 value exist in the regular Renderer all along but not exposed in the inspector.) The content of Sorting Layer drop down will be just like what you see on your SpriteRenderer minus the last row "Add Sorting Layer..."

I put together other's code on exposing these 2 values on the inspector and added more functionality like mimicking drop down menu of SpriteRenderer's and used SerializedProperty to enable undo/revert to prefab which took me quite a few hours so I thought about sharing with anyone that might having the same problem as me. Now you can freely arrange your Spine character anywhere with your other Sprite objects. In the same layer, MeshRenderer still can draw on top of each other using Z value as usual. (Not the case with SpriteRenderer where Z is ignored)

The acknowledgement of various scripts used to make this is on the comment section of the code. Just put this code in your Editor folder and it should work.

using UnityEngine;
#if UNITY_EDITOR
using UnityEditor;
using UnityEditorInternal;
using System.Reflection;
using System;
#endif

//Expose SortingLayer & SortingOrder on MeshRenderer
//With nice drop down and revert to prefab functionality.

//Base exposing code by neror http://forum.unity3d.com/threads/212006-Drawing-order-of-Meshes-and-Sprites
//Get all sorting layer name and ID by guavaman & Ivan.Murashko http://answers.unity3d.com/questions/585108/how-do-you-access-sorting-layers-via-scripting.html
//Sorting Layer drop down menu, bold text on prefab override, revert to prefab and instant update on Order change functionality by 5argon

[CustomEditor(typeof(MeshRenderer))]

public class MeshRendererSortingLayersEditor : Editor
{

public override void OnInspectorGUI()
{

    base.OnInspectorGUI();

    serializedObject.Update();

    SerializedProperty sortingLayerID = serializedObject.FindProperty("m_SortingLayerID");
    SerializedProperty sortingOrder = serializedObject.FindProperty("m_SortingOrder");

    MeshRenderer renderer = target as MeshRenderer;

    Rect firstHoriz = EditorGUILayout.BeginHorizontal();

    EditorGUI.BeginChangeCheck();

    EditorGUI.BeginProperty(firstHoriz,GUIContent.none,sortingLayerID);

    string[] layerNames = GetSortingLayerNames();
    int[] layerID = GetSortingLayerUniqueIDs();

    int selected = -1;
    //What is selected?
    int sID = sortingLayerID.intValue;
    for(int i = 0 ; i < layerID.Length ; i++)
    {
        //Debug.Log(sID + " " + layerID[i]);
        if(sID == layerID[i])
        {
            selected = i;
        }
    }

    if(selected == -1)
    {
        //Select Default.
        for(int i = 0 ; i < layerID.Length ; i++)
        {
            if(layerID[i] == 0)
            {
                selected = i;
            }
        }
    }

    selected = EditorGUILayout.Popup("Sorting Layer" ,selected,layerNames);

    //Translate to ID
    sortingLayerID.intValue = layerID[selected];


    EditorGUI.EndProperty();

    EditorGUILayout.EndHorizontal();

    EditorGUILayout.BeginHorizontal();
    EditorGUI.BeginChangeCheck();

    EditorGUILayout.PropertyField(sortingOrder,new GUIContent("Order in Layer"));


    EditorGUILayout.EndHorizontal();
    serializedObject.ApplyModifiedProperties();
}

public string[] GetSortingLayerNames() {
    Type internalEditorUtilityType = typeof(InternalEditorUtility);
    PropertyInfo sortingLayersProperty = internalEditorUtilityType.GetProperty("sortingLayerNames", BindingFlags.Static | BindingFlags.NonPublic);
    return (string[])sortingLayersProperty.GetValue(null, new object[0]);
}

public int[] GetSortingLayerUniqueIDs() {
    Type internalEditorUtilityType = typeof(InternalEditorUtility);
    PropertyInfo sortingLayerUniqueIDsProperty = internalEditorUtilityType.GetProperty("sortingLayerUniqueIDs", BindingFlags.Static | BindingFlags.NonPublic);
    return (int[])sortingLayerUniqueIDsProperty.GetValue(null, new object[0]);
}

}