Luk 11:11-13 If a son shall ask bread of any of you that is a father, will he give him a stone? or if he ask a fish, will he for a fish give him a serpent? Or if he shall ask an egg, will he offer him a scorpion? If ye then, being evil, know how to give good gifts unto your children: how much more shall your heavenly Father give the Holy Spirit to them that ask him?
This passage is at the end of the familiar passage that talks about asking and receiving "ask and it shall be given you." After Jesus finishes exhorting the disciples to pray, he gives an example they would have been familiar with, the example of a father and his child. Jesus describes an earthly father that gives his child the things he daily needs. Then the Lord compares the earthly father to our heavenly Father. If the earthly father can give good gifts so much more will our heavenly Father.
1Th 2:10-12 Ye are witnesses, and God also, how holily and justly and unblameably we behaved ourselves among you that believe: As ye know how we exhorted and comforted and charged every one of you, as a father doth his children, That ye would walk worthy of God, who hath called you unto his kingdom and glory.
These verses do not reference our Heavenly father, but they do discuss what an earthly father does. He exhorts (encourages), comforts and charges (commands) his children.
Heb 12:5-11 And ye have forgotten the exhortation which speaketh unto you as unto children, My son, despise not thou the chastening of the Lord, nor faint when thou art rebuked of him: For whom the Lord loveth he chasteneth, and scourgeth every son whom he receiveth. If ye endure chastening, God dealeth with you as with sons; for what son is he whom the father chasteneth not? But if ye be without chastisement, whereof all are partakers, then are ye bastards, and not sons. Furthermore we have had fathers of our flesh which corrected us, and we gave them reverence: shall we not much rather be in subjection unto the Father of spirits, and live? For they verily for a few days chastened us after their own pleasure; but he for our profit, that we might be partakers of his holiness. Now no chastening for the present seemeth to be joyous, but grievous: nevertheless afterward it yieldeth the peaceable fruit of righteousness unto them which are exercised thereby.
These verse discuss how God deals with his children compared with how an earthly father deals with his children. As Christians we are to not to despise the chastening (Correcting; afflicting for correction*) that the Lord gives us. The Lord is shown as a loving Father that chasteneth and scourgeth (To afflict greatly; to harass, torment or injure.*) his children. The encouragement is that if the Lord is chastening you then you are His child. Then the comparison is made to our earthly father. Our father corrected and chastened us for a small amount of time for his own pleasure, but our heavenly Father does it so that we could be more like Him. That chastening is never pleasant, but it does result in righteousness.
So what can we learn from these passages? The Luke and Hebrews passages both compare our heavenly Father with an earthly father. Both the earthly father and the heavenly Father give gifts to their children and chasten their children. The I Thess. passage describes an earthly father that encourages, comforts, and commands his children. So as parents do we have these characteristics? Could we be described as giving, chastening, encouraging, comforting, commanding?
*Definitions are from http://av1611.com/kjbp/kjv-dictionary/kjv-dictionary-index.html