My first thought would be that a sheer basque and skirt ensemble would have awkward shadows where the bodice overlaps the upper skirt (unless perhaps the whole skirt were flounced to make a regular pattern of it).
Searching through the fashion descriptions, I'm finding several mid-50s references to contrasting white 'basques' for light summer wear; these appear to be for wearing with a skirt, not as outerwear over another bodice (silk basques over lightweight skirts also seem to pop up). There aren't many illustrations of the former, however, so I'm uncertain about how "basque" is meant in context: it could just be a separate bodice, not necessarily extending below the waist. There's also some suggestions that sheer cotton dresses (organdy in particular) are not made up with basques, but barege (which, if I recall correctly is a semi-sheer wool or wool/silk material) is frequently named for basques. Perhaps someone else can make sense of it:
From Graham's American Monthly Magazine of Literature, Art, and Fashion
"[Detailed description of flounced silk skirt] The basque was trimmed in the same manner but for the warm days we should advise a white basque with pink or light green ribbons."
"Another dress of very novel and pretty effect of fawn colored barege with three flounces embroidered in a deep scallop with silk of the same color. Between each of the barege flounces is a flounce of plaid silk also scalloped in silk. When a white basque is not worn with this dress the basque made for it is of the plaid silk the same as that which compose the flounces."
"Light materials are of course prevalent this month, and flounces have established their reign. Moire antique, however, has not been laid aside but then it is only worn as a skirt; thanks to the universal fashion of white muslin basques or waists, rich silks can be worn this year Many prefer this to muslins and bareges which are so soon tumbled and which require so much care in the accessories and the underskirts There are however some beautiful light materials this summer: barege, of course, mousseline de soie, crepe de Paris, grenadine and chali (challis?), which is only a revival, but one much to be admired for it is a beautiful tissue and most becoming from its graceful folds. Besides there are jaconets, and organdies, and lawns of very beautiful pattern... A very good innovation for hot weather is to line the barege basques with soft fine mull muslin; it is better than Florence silk for this purpose at this season... Dresses are almost all made with basques--still for very young ladies we think the plain or full corsage is more suitable..."The London and Paris Ladies' Magazine of Fashion
"... the bodies of barege and organdy dresses are made full without basques; the flounces of organdys are edged by a small guipure or lace edging the top flounce, left open in front as a tunic which gives the effect of a basque... When the barege dresses are without basques the bodies are full, with ceinture of wide ribbon and floating ends, but the basques are more generally preferred. There is a new material of still slighter texture than barege, but less flimsy; they as well as bareges are worn over silk skirts flounced which is preferred to lining the flounce."The New Monthly Belle Assemblee
"Gowns in barege
, and grenadine
are made with flounces... As for the corsages of the gowns, those in thin materials are either a la vierge
or full bodies gathered at the waist and shoulders or a sort of vest with basquines
; but this last is very difficult to make and rarely fits well. The basques
are much easier to succeed in and produce the same effect. Most of the corsages
, particularly those in silk, are made quite high."