尝试理解一下，首先，我认为，您的分析是有一定道理的。不过，这里应该涉及了一些语法术语表述问题。首先是补足语（complement)问题，这个概念的外延比较大。

例如The Oxford Dictionary of English Grammar对complement（补足语）的解释:

More widely,any element needed to 'complete' an adjective,preposition,verb,or noun.Complements of adjectives include preposional phrases,e.g. fond of chocolate,to-infinitive(clause),e.g. sorry to hear your news, and clauses,e.g. sorry that you're ill.Complements of prepositions are usually noun phrases,e.g. out of order,in the bag.The complement of a verb,in this wider sense,is a very unspecific term,and can include not only subject complements and object complements,but also adverbials,objects,non-finite verbs,and entire sentence predicates apart from the verb itself.In most models the subject is not regarded as a complement of the verb;CaGEL is an exception.The words following a head noun,particularly an abstract noun in some types of noun phrase,are sometimes analysed as the complement of a noun(e.g. They deplored her lack of remorse:They deplored her lack is impossible).

另外，The Oxford Dictionary of English Grammar(second edition)对complement(补足语）有这样的解释：

More narrowly,one of the five elements of clause structure,along with subject,verb,object,and adverbial，所以，狭义地讲，补足语应该指分句内中心成分，即主语补足语和宾语补足语。所以，这里出现了另外一个术语complementation，章振邦和张克礼将其解释为补足成分，而非补足语。

The Oxford Dictionary of English Grammar也提及到了此术语:

Complementation:The addition of a complement to a linguistic unit.For most linguists this is a syntactic concept,but note the semantic perspective in the quotation below:

1985 R.Quirk et al.  We reserve the term complementation(as distinct from complement) for the function of a part of a phrase or clause which follows a word,and completes the specification of a meaning relationship which that word implies.

张克礼这样解释complementation（补足成分）：补足成分不同于补足语（complements)。补足语是5个分句成分（S,V,C,O,A)之一(C)，和其他分句成分一样是独立的分句成分；补足成分结构层次低于补足语，不是独立的分句成分，而是分句成分的组成部分，即和其所修饰或搭配的分句成分一起充当分句成分。所以，补足成分应该属于词组内成分。

章振邦在谈及“介词补足成分”时也提到:“当代有些语法学家避免采用'介词宾语'这一传统术语，改名为介词补语，因为介词通常不能单独使用，它必须带有补足成分才能表示一定意义。但是，这种补足成分如果命名为'补语'，似乎也未尽妥善，因为补语也是一种分句成分。有鉴于此，我们做了改动，既不叫'介词宾语'，也不叫'介词补语'，而叫'介词补足成分'。另外他还有其他论述，如，“不定式分句可作形容词补足成分（adjective complementation)，在语法层次上作为形容词词组的组成部分。”再如，“一切介词，不论是简单介词还是复杂介词，不论这个介词是主句动词的组成部分，或不是主句动词的组成部分，都能用-ing分词分句作补足成分。”

所以，狭义地讲:

I got tired of hearing my father complain about my job.这个句子似乎可以这样解释：-ing分词分句hearing my father complain about my job作介词of的补足成分（complementation），而介词词组of hearing my father complain about my job作形容词tired的补足成分，在语法层次上是形容词词组的组成部分，这里的got解释为连系动词，所以形容词词组tired of hearing my father complain about my job在分句中作主语补足语，整个分句是一个主+动+补（SVC）结构。或者广义地讲，把介词词组 of hearing my father complain about my job解释为形容词tired的补足语。