どんな雲にも銀の裏地がついている; 「苦は楽の種」The gloss 裏地 matches the main meaning of "lining" given in English-English dictionaries—"material that lines or that is used to line especially the inner surface of something (as a garment)" (Merriam-Webster's Collegiate). But I had always understood "silver lining" to a refer to a silver or white edge around a dark cloud, not to some material lining the cloud's "inner surface," whatever that might be.
《諺》苦あれば楽あり《＜雲はみな銀の裏地（雲の上に輝く光）がついている》The explanation 雲の上に輝く光 doesn't match my interpretation, either; a cloud's silver lining could be at the sides or bottom of the cloud as well as above it, couldn't it?
《諺》 どんな雲にもみな銀の裏がついている 《憂いの反面には喜びがある》.Several English-Japanese dictionaries do agree with my interpretation, but only in their entries for "silver lining," not in their translations of the entire proverb. For example:
silver lining 黒い雲からのぞく銀色のふち; 不幸の中に見える明るい希望. (エクシード英和)English-English dictionaries are not much help in clearing up the confusion, as most define only the extended meaning of "silver lining." The following is typical:
silver lining 雲の明るいへり; 《不幸中などでの》明るい希望, 《前途の》光明. [諺 Every CLOUD has a ～. から] (リーダーズ)
silver liningOnly two that I checked also, helpfully, give the literal sense:
NOUN: A hopeful or comforting prospect in the midst of difficulty.
ETYMOLOGY: From the proverb "Every cloud has a silver lining".
silver liningNote the exact repetition of phrasing from Merriam-Webster's Unabridged (both the second and third editions); such apparent copying is generally less common in dictionaries published in English-speaking countries than in those published in Japan. Collins English, for example, uses "comforting" instead of "consoling," and the definition is different in other ways as well:
1: a white edge on a cloud
2 : a consoling or hopeful prospect
a consoling or hopeful prospect. [from the metaphorical use of the phrase every cloud has a silver lining, i.e. a white edge]
(New Penguin English)
silver liningWebster's New World uses a different paraphrase:
a comforting or hopeful aspect of an otherwise desperate or unhappy situation (esp. in the phrase every cloud has a silver lining)
silver liningMacquarie is quite different:
some basis of hope or some comforting aspect in the midst of despair, misfortune, etc.
Colloquial some pleasing or beneficial component of a generally adverse situation: *Then suddenly, within a year, came the silver lining. - FRANK HARDY, 1950
(April 26, 2003)