This is what I came up with. Sorry if it's a bit huge, but I thought it might be useful to make it decent. I tested it and it seems to work fine. Let me know if it doesn't work correctly.

using UnityEngine;
using System.Collections;
using System;

public class TimeOfDay : MonoBehaviour
{
   public float timePerDay = 1140.0f; // In seconds
   public float sunrise = 6.0f; // In hours
   public float sunset = 17.0f; // In hours
   public float hoursPerDay = 24.0f; // In hours

   public Color dayAmbientColor;
   public Color dayBackgroundColor;
   public Color nightAmbientColor;
   public Color nightBackgroundColor;

   public float currentTime = 0.0f;

   private float NightDuration
   {
       get { return timePerDay - RelativeSunset + RelativeSunrise; }
   }

   private float DayDuration
   {
       get { return RelativeSunset - RelativeSunrise; }
   }

   private float RelativeSunrise
   {
       get { return timePerDay * (sunrise / hoursPerDay); }
   }

   private float RelativeSunset
   {
       get { return timePerDay * (sunset / hoursPerDay); }
   }

   private float Midday
   {
       get { return (DayDuration * 0.5f) + RelativeSunrise; }
   }

   private float Midnight
   {
       get { return Mathf.PingPong((NightDuration * 0.5f) + RelativeSunset, timePerDay); }
   }

   // Use this for initialization
   public void Start ()
   {

   }

   // Update is called once per frame
   public void Update ()
   {
      currentTime += Time.deltaTime;

      // If we have reached the end of day start the cycle over
      if (currentTime >= timePerDay)
          currentTime = currentTime - timePerDay; // Keep the extra time

      Color currentAmbientColor = Color.black;
      Color currentBackgroundColor = Color.black;

      float midday = Midday;
      float midnight = Midnight;
      float sampleTime = 0.0f;

      float minutesPastMidnight = (currentTime > midnight && currentTime < timePerDay) ? timePerDay - currentTime : timePerDay - midnight + currentTime;
      if (currentTime > midday && currentTime <= midnight)
      {
          sampleTime = (currentTime - midday) / DayDuration;
          Debug.Log("Sample Day: " + sampleTime);
      }
      else if (minutesPastMidnight >= 0)
      {
          sampleTime = 1.0f - (minutesPastMidnight / NightDuration);
      }

      currentAmbientColor = Color.Lerp(dayAmbientColor, nightAmbientColor, sampleTime);
      currentBackgroundColor = Color.Lerp(dayBackgroundColor, nightBackgroundColor, sampleTime);

      RenderSettings.ambientLight = currentAmbientColor;
      Camera.main.backgroundColor = currentBackgroundColor;
   }
}